Details

analyze324.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Rules

708×	`associate-+l+_binary64_2398`
673×	`associate-+r+_binary64_2397`
459×	`div-sub_binary64_2470`
372×	`*-commutative_binary64_2396`
272×	`distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414`
210×	`sub-neg_binary64_2458`
202×	`distribute-rgt-out_binary64_2418` `associate-l_binary64_2406`
194×	`times-frac_binary64_2471`
190×	`associate-r_binary64_2405`
183×	`unsub-neg_binary64_2459`
164×	`+-commutative_binary64_2395`
103×	`neg-mul-1_binary64_2461`
92×	`distribute-lft-out_binary64_2416`
91×	`associate-/r/_binary64_2411`
89×	`neg-sub0_binary64_2460`
88×	`associate-/l*_binary64_2410`
68×	`cancel-sign-sub-inv_binary64_2431`
56×	`associate-/r*_binary64_2409`
45×	`associate-*l/_binary64_2408`
39×	`associate-*r/_binary64_2407`
35×	`associate--r+_binary64_2401`
33×	`distribute-rgt-neg-out_binary64_2425`
30×	`associate-/l/_binary64_2412`
28×	`distribute-frac-neg_binary64_2428`
27×	`distribute-lft-neg-out_binary64_2424`
26×	`associate--r-_binary64_2404`
25×	`associate-+l-_binary64_2400`
24×	`distribute-lft-neg-in_binary64_2422` `associate-+r-_binary64_2399`
20×	`distribute-rgt-neg-in_binary64_2423`
18×	`div0_binary64_2446` `distribute-neg-in_binary64_2426`
16×	`distribute-neg-frac_binary64_2429`
6×	`sub0-neg_binary64_2452` `swap-sqr_binary64_2432`
4×	`distribute-neg-out_binary64_2427`
3×	`mul-1-neg_binary64_2457` `+-rgt-identity_binary64_2450` `distribute-lft1-in_binary64_2420`
2×	`sqr-neg_binary64_2479` `associate--l+_binary64_2402`
1×	`1-exp_binary64_2509`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `log-div_binary64_2552` `log-prod_binary64_2551` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow3_binary64_2531` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow1_binary64_2523` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `exp-prod_binary64_2517` `div-exp_binary64_2516` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-unmult_binary64_2502` `cube-mult_binary64_2495` `cube-div_binary64_2494` `cube-prod_binary64_2493` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `/-rgt-identity_binary64_2456` `-rgt-identity_binary64_2455` `-lft-identity_binary64_2454` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `sqr-pow_binary64_2437` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `unswap-sqr_binary64_2433` `cancel-sign-sub_binary64_2430` `distribute-rgt1-in_binary64_2421` `distribute-rgt-out--_binary64_2419` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate--l-_binary64_2403`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	172
1	100	172
2	349	172
3	1379	172
4	3193	172
5	4121	172
6	4980	172
7	4894	172
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample41.0ms (0.1%)

Algorithm

1×

intervals

Results

11.0ms	194×	body	128	valid
5.0ms	256×	pre	128	true
5.0ms	23×	body	1024	valid
4.0ms	22×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify78.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64_2471`
817×	`distribute-rgt-in_binary64_2415`
748×	`distribute-lft-in_binary64_2414`
576×	`sub-neg_binary64_2458`
537×	`div-sub_binary64_2470`
255×	`+-commutative_binary64_2395`
194×	`associate-+l+_binary64_2398`
187×	`*-commutative_binary64_2396`
183×	`associate-+r+_binary64_2397`
142×	`associate-/l*_binary64_2410`
137×	`unsub-neg_binary64_2459`
117×	`neg-mul-1_binary64_2461`
115×	`associate-*l/_binary64_2408`
111×	`neg-sub0_binary64_2460`
104×	`distribute-rgt-out_binary64_2418`
103×	`associate-l_binary64_2406`
100×	`associate-r_binary64_2405`
98×	`associate-*r/_binary64_2407`
60×	`distribute-lft-out_binary64_2416`
55×	`associate-+l-_binary64_2400`
44×	`associate--r+_binary64_2401`
42×	`associate-/r*_binary64_2409`
33×	`cancel-sign-sub-inv_binary64_2431` `distribute-frac-neg_binary64_2428` `distribute-rgt-neg-out_binary64_2425`
32×	`associate--l+_binary64_2402`
28×	`associate-/l/_binary64_2412` `associate-/r/_binary64_2411`
27×	`distribute-lft-neg-out_binary64_2424`
25×	`associate-+r-_binary64_2399`
24×	`mul0-rgt_binary64_2448`
23×	`mul0-lft_binary64_2447`
21×	`distribute-rgt-neg-in_binary64_2423`
20×	`distribute-lft-neg-in_binary64_2422`
18×	`distribute-neg-out_binary64_2427`
14×	`distribute-neg-in_binary64_2426`
12×	`distribute-neg-frac_binary64_2429`
10×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
8×	`distribute-rgt-out--_binary64_2419`
6×	`sub0-neg_binary64_2452` `div0_binary64_2446` `distribute-lft1-in_binary64_2420`
5×	`distribute-rgt1-in_binary64_2421`
4×	`associate--r-_binary64_2404`
3×	`associate--l-_binary64_2403`
2×	`mul-1-neg_binary64_2457` `swap-sqr_binary64_2432`
1×	`1-exp_binary64_2509` `sqr-neg_binary64_2479` `remove-double-neg_binary64_2453` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `log-div_binary64_2552` `log-prod_binary64_2551` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow3_binary64_2531` `unpow2_binary64_2530` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow1_binary64_2523` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `exp-prod_binary64_2517` `div-exp_binary64_2516` `rec-exp_binary64_2515` `prod-exp_binary64_2514` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `exp-sum_binary64_2511` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-unmult_binary64_2502` `cube-mult_binary64_2495` `cube-div_binary64_2494` `cube-prod_binary64_2493` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `/-rgt-identity_binary64_2456` `+-lft-identity_binary64_2449` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `sqr-pow_binary64_2437` `difference-of-sqr--1_binary64_2436` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `unswap-sqr_binary64_2433` `cancel-sign-sub_binary64_2430` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	43
2	106	43
3	409	43
4	1505	43
5	2316	43
6	3123	43
7	4954	43
8	4973	43
9	5371	43

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

29.2b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 alpha beta) (*.f64 2 i))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
2.7b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
23.2b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite388.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

15.5b

Rules

54×	`times-frac_binary64_2471`
48×	`*-un-lft-identity_binary64_2465`
26×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
18×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
14×	`associate-/r/_binary64_2411`
12×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
11×	`add-log-exp_binary64_2504` `distribute-lft-out_binary64_2416`
10×	`associate-/l*_binary64_2410`
9×	`associate-/l/_binary64_2412`
7×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `associate-/r*_binary64_2409`
4×	`pow1_binary64_2526` `frac-times_binary64_2475` `sum-log_binary64_2556`
3×	`flip3--_binary64_2469` `flip--_binary64_2440`
2×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-l/_binary64_2408` `associate-r/_binary64_2407` `+-commutative_binary64_2395`
1×	`associate-+l+_binary64_2398`

Counts

4 → 124

Calls

4 calls:

36.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
26.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
16.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
6.0ms	(+.f64 (+.f64 alpha beta) (*.f64 2 i))

Compiler

Compiled 5852 to 2957 computations (49.5% saved)

series3.7s (11.2%)

Error

0.5b

Counts

4 → 97

Calls

4 calls:

1.7s	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.1s	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
391.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
155.0ms	(+.f64 (+.f64 alpha beta) (*.f64 2 i))

Compiler

Compiled 15513 to 11814 computations (23.8% saved)

simplify210.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

628×	`times-frac_binary64_2471`
368×	`distribute-rgt-in_binary64_2415`
353×	`distribute-lft-in_binary64_2414`
243×	`+-commutative_binary64_2395`
184×	`associate-+r+_binary64_2397`
151×	`*-commutative_binary64_2396`
143×	`sub-neg_binary64_2458`
104×	`associate-*r/_binary64_2407`
70×	`distribute-neg-in_binary64_2426`
65×	`cancel-sign-sub-inv_binary64_2431`
60×	`associate-/l*_binary64_2410`
41×	`sqr-pow_binary64_2437`
40×	`neg-sub0_binary64_2460`
38×	`distribute-rgt-out_binary64_2418`
37×	`neg-mul-1_binary64_2461`
35×	`associate-/l/_binary64_2412` `associate-/r*_binary64_2409`
33×	`div-sub_binary64_2470`
32×	`associate--l+_binary64_2402`
27×	`associate--r+_binary64_2401`
20×	`distribute-lft-out_binary64_2416`
17×	`distribute-rgt-neg-in_binary64_2423`
14×	`distribute-neg-frac_binary64_2429`
12×	`distribute-lft-neg-in_binary64_2422`
11×	`unpow3_binary64_2531` `/-rgt-identity_binary64_2456` `associate-r_binary64_2405`
10×	`log-div_binary64_2552`
9×	`cube-mult_binary64_2495` `cube-div_binary64_2494` `associate-l_binary64_2406`
8×	`unpow2_binary64_2530` `unpow1_binary64_2523` `unswap-sqr_binary64_2433`
7×	`-rgt-identity_binary64_2455` `-lft-identity_binary64_2454`
6×	`swap-sqr_binary64_2432`
5×	`associate-/r/_binary64_2411`
4×	`exp-prod_binary64_2517` `prod-exp_binary64_2514` `cube-prod_binary64_2493` `mul-1-neg_binary64_2457` `distribute-rgt1-in_binary64_2421`
3×	`log-prod_binary64_2551` `exp-sum_binary64_2511` `cube-unmult_binary64_2502` `distribute-lft-neg-out_binary64_2424` `distribute-rgt-out--_binary64_2419` `associate-*l/_binary64_2408` `associate-+r-_binary64_2399`
2×	`associate-+l+_binary64_2398`
1×	`exp-lft-sqr_binary64_2520` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `unsub-neg_binary64_2459` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `associate--l-_binary64_2403`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `difference-of-sqr--1_binary64_2436` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft1-in_binary64_2420` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate--r-_binary64_2404` `associate-+l-_binary64_2400`

Counts

221 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	765	13149
1	2344	12774
2	5192	12774

prune643.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Error

0.1b

Counts

193 → 5

Compiler

Compiled 10814 to 5809 computations (46.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
2.7b	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite359.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

48×	`*-un-lft-identity_binary64_2465`
45×	`add-sqr-sqrt_binary64_2487`
35×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
21×	`associate-r_binary64_2405`
20×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417` `associate-/l/_binary64_2412` `associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `pow1_binary64_2526` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `associate-/r/_binary64_2411` `associate-/l*_binary64_2410`
4×	`distribute-lft-out_binary64_2416` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-times_binary64_2475` `associate-l/_binary64_2408` `associate-l*_binary64_2406`
3×	`div-inv_binary64_2462`
2×	`unswap-sqr_binary64_2433` `associate-*r/_binary64_2407` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
1×	`sum-log_binary64_2556` `+-commutative_binary64_2395` `pow-prod-down_binary64_2536` `*-commutative_binary64_2396` `div-sub_binary64_2470` `flip3--_binary64_2469` `flip--_binary64_2440`

Counts

4 → 129

Calls

4 calls:

29.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
27.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 5642 to 2885 computations (48.9% saved)

series4.0s (11.9%)

Error

0.1b

Counts

4 → 101

Calls

4 calls:

1.7s	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
1.1s	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
381.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
335.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 16802 to 12833 computations (23.6% saved)

simplify204.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

659×	`times-frac_binary64_2471`
321×	`distribute-rgt-in_binary64_2415`
311×	`distribute-lft-in_binary64_2414`
265×	`+-commutative_binary64_2395`
192×	`associate-+r+_binary64_2397`
181×	`*-commutative_binary64_2396`
175×	`sub-neg_binary64_2458`
136×	`associate-*r/_binary64_2407`
83×	`distribute-neg-in_binary64_2426`
67×	`cancel-sign-sub-inv_binary64_2431`
65×	`associate-/l*_binary64_2410`
48×	`neg-sub0_binary64_2460`
44×	`neg-mul-1_binary64_2461`
43×	`div-sub_binary64_2470`
41×	`sqr-pow_binary64_2437` `distribute-rgt-out_binary64_2418`
39×	`associate--l+_binary64_2402`
34×	`associate--r+_binary64_2401`
29×	`associate-/r*_binary64_2409`
22×	`distribute-lft-out_binary64_2416`
16×	`distribute-neg-frac_binary64_2429`
15×	`distribute-rgt-neg-in_binary64_2423`
11×	`unpow3_binary64_2531`
10×	`associate-l_binary64_2406`
9×	`log-div_binary64_2552` `cube-mult_binary64_2495` `distribute-lft-neg-in_binary64_2422` `associate-r_binary64_2405`
8×	`unpow2_binary64_2530` `unpow1_binary64_2523` `cube-div_binary64_2494` `/-rgt-identity_binary64_2456` `swap-sqr_binary64_2432`
7×	`cube-prod_binary64_2493` `unswap-sqr_binary64_2433`
6×	`exp-prod_binary64_2517` `*-rgt-identity_binary64_2455`
5×	`log-prod_binary64_2551`
4×	`mul-1-neg_binary64_2457` `distribute-rgt1-in_binary64_2421`
3×	`cube-unmult_binary64_2502` `distribute-lft-neg-out_binary64_2424` `associate-/l/_binary64_2412` `associate-*l/_binary64_2408` `associate-+r-_binary64_2399`
2×	`exp-sum_binary64_2511` `*-lft-identity_binary64_2454` `difference-of-squares_binary64_2434` `associate-+l+_binary64_2398`
1×	`prod-exp_binary64_2514` `exp-diff_binary64_2513` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `unsub-neg_binary64_2459` `difference-of-sqr-1_binary64_2435` `distribute-rgt-out--_binary64_2419` `associate-/r/_binary64_2411`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `unpow1/2_binary64_2529` `pow-plus_binary64_2528` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `rem-sqrt-square_binary64_2478` `rem-square-sqrt_binary64_2477` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `pow-sqr_binary64_2438` `difference-of-sqr--1_binary64_2436` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft1-in_binary64_2420` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate-+l-_binary64_2400`

Counts

230 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	817	12610
1	2475	12168
2	5151	12168

prune570.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	194	5	199

Error

0.1b

Counts

199 → 5

Compiler

Compiled 10841 to 6044 computations (44.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
2.7b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)) 1)
10.6b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))

rewrite468.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

67×	`*-un-lft-identity_binary64_2465`
41×	`times-frac_binary64_2471`
38×	`add-sqr-sqrt_binary64_2487`
28×	`cbrt-prod_binary64_2496`
26×	`associate-r_binary64_2405`
25×	`add-cube-cbrt_binary64_2500`
22×	`unpow-prod-down_binary64_2544` `cube-prod_binary64_2493`
19×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416`
10×	`associate-/r/_binary64_2411`
8×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504`
5×	`div-inv_binary64_2462` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
4×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-l_binary64_2406` `difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417` `pow-exp_binary64_2533` `rem-cube-cbrt_binary64_2488`
3×	`pow-unpow_binary64_2542`
2×	`cube-div_binary64_2494` `unpow3_binary64_2531` `cube-mult_binary64_2495` `sqr-pow_binary64_2437` `frac-times_binary64_2475` `unswap-sqr_binary64_2433` `associate-*l/_binary64_2408`
1×	`pow1/3_binary64_2547` `cbrt-div_binary64_2497` `rem-cbrt-cube_binary64_2489` `sum-log_binary64_2556` `+-commutative_binary64_2395` `pow-prod-down_binary64_2536` `associate-r/_binary64_2407` `-commutative_binary64_2396` `pow-pow_binary64_2537` `pow-to-exp_binary64_2534`

Counts

4 → 146

Calls

4 calls:

26.0ms	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)
23.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
21.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)) 1)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))

Compiler

Compiled 7401 to 4604 computations (37.8% saved)

series5.8s (17.3%)

Error

0.1b

Counts

4 → 103

Calls

4 calls:

2.0s	(pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)
1.8s	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3)) 1)
1.2s	(cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))) 3))
381.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))

Compiler

Compiled 20354 to 15879 computations (22% saved)

simplify264.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

383×	`+-commutative_binary64_2395`
304×	`associate-+r+_binary64_2397`
279×	`*-commutative_binary64_2396`
251×	`distribute-rgt-in_binary64_2415`
208×	`associate-*r/_binary64_2407`
192×	`sub-neg_binary64_2458`
103×	`sqr-pow_binary64_2437`
98×	`distribute-neg-in_binary64_2426`
90×	`associate-/l*_binary64_2410`
89×	`cancel-sign-sub-inv_binary64_2431`
57×	`distribute-rgt-out_binary64_2418`
49×	`neg-sub0_binary64_2460`
46×	`associate--l+_binary64_2402`
44×	`neg-mul-1_binary64_2461`
40×	`associate--r+_binary64_2401`
39×	`unswap-sqr_binary64_2433`
35×	`unpow3_binary64_2531`
34×	`cube-mult_binary64_2495`
33×	`associate-/r*_binary64_2409`
23×	`times-frac_binary64_2471`
22×	`cube-div_binary64_2494`
21×	`distribute-lft-out_binary64_2416`
17×	`rem-cbrt-cube_binary64_2489` `distribute-lft-in_binary64_2414`
15×	`distribute-rgt-neg-in_binary64_2423`
14×	`swap-sqr_binary64_2432`
13×	`exp-prod_binary64_2517` `div-sub_binary64_2470`
12×	`log-prod_binary64_2551`
11×	`associate-r_binary64_2405`
10×	`cube-prod_binary64_2493`
9×	`unpow1_binary64_2523` `distribute-neg-frac_binary64_2429` `distribute-lft-neg-in_binary64_2422`
8×	`unpow2_binary64_2530`
7×	`mul-1-neg_binary64_2457`
6×	`log-div_binary64_2552` `associate-l_binary64_2406`
5×	`*-rgt-identity_binary64_2455`
4×	`/-rgt-identity_binary64_2456` `pow-sqr_binary64_2438` `distribute-lft-neg-out_binary64_2424` `distribute-rgt1-in_binary64_2421` `associate-+r-_binary64_2399`
3×	`log-pow_binary64_2554` `rem-sqrt-square_binary64_2478` `difference-of-sqr--1_binary64_2436` `associate-/l/_binary64_2412`
2×	`exp-sum_binary64_2511` `cube-unmult_binary64_2502` `rem-cube-cbrt_binary64_2488` `-lft-identity_binary64_2454` `difference-of-squares_binary64_2434` `distribute-rgt-out--_binary64_2419` `associate-l/_binary64_2408`
1×	`unpow1/2_binary64_2529` `pow-plus_binary64_2528` `prod-exp_binary64_2514` `1-exp_binary64_2509` `exp-1-e_binary64_2508` `rem-3cbrt-lft_binary64_2490` `rem-square-sqrt_binary64_2477` `difference-of-sqr-1_binary64_2435`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-rec_binary64_2553` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-diff_binary64_2513` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `unsub-neg_binary64_2459` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `*-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft1-in_binary64_2420` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate-/r/_binary64_2411` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate-+l-_binary64_2400` `associate-+l+_binary64_2398`

Counts

249 → 219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1125	16814
1	3504	16004
2	4984	16004

prune822.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	219	5	224

Error

0.1b

Counts

224 → 5

Compiler

Compiled 13229 to 7957 computations (39.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))
0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))
1.3b	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) -1)
4.0b	(+.f64 (pow.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) 2) -1)

rewrite624.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

70×	`*-un-lft-identity_binary64_2465`
55×	`add-sqr-sqrt_binary64_2487`
52×	`associate-r_binary64_2405`
42×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
14×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out_binary64_2416`
8×	`add-log-exp_binary64_2504` `pow1_binary64_2526` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-l_binary64_2406` `difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
5×	`difference-of-sqr--1_binary64_2436`
4×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-times_binary64_2475` `unswap-sqr_binary64_2433` `associate-*l/_binary64_2408` `associate-/r/_binary64_2411`
2×	`sum-log_binary64_2556` `+-commutative_binary64_2395` `pow-prod-down_binary64_2536` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `associate-r/_binary64_2407` `div-inv_binary64_2462` `-commutative_binary64_2396`
1×	`unpow-prod-down_binary64_2544` `unpow2_binary64_2530` `sqr-pow_binary64_2437`

Counts

4 → 129

Calls

4 calls:

27.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) -1)
21.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))
20.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))
17.0ms	(+.f64 (pow.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) 2) -1)

Compiler

Compiled 9691 to 5656 computations (41.6% saved)

series7.1s (21.2%)

Error

0.1b

Counts

4 → 96

Calls

4 calls:

2.9s	(+.f64 (pow.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) 2) -1)
2.7s	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha))) (+.f64 2 (+.f64 (+.f64 beta (*.f64 2 i)) alpha))) -1)
457.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))
229.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta (.f64 2 i)) alpha)))

Compiler

Compiled 25532 to 18777 computations (26.5% saved)

simplify235.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

345×	`+-commutative_binary64_2395`
287×	`*-commutative_binary64_2396`
265×	`associate-+r+_binary64_2397`
239×	`distribute-rgt-in_binary64_2415`
224×	`distribute-lft-in_binary64_2414`
219×	`associate-*r/_binary64_2407`
153×	`sub-neg_binary64_2458`
83×	`distribute-neg-in_binary64_2426`
81×	`associate-/r/_binary64_2411`
80×	`associate-/l*_binary64_2410`
65×	`cancel-sign-sub-inv_binary64_2431`
50×	`associate-/r*_binary64_2409`
49×	`sqr-pow_binary64_2437`
45×	`neg-sub0_binary64_2460`
42×	`distribute-rgt-out_binary64_2418`
39×	`neg-mul-1_binary64_2461`
37×	`times-frac_binary64_2471`
32×	`unswap-sqr_binary64_2433` `associate--r+_binary64_2401`
30×	`associate--l+_binary64_2402`
20×	`associate-/l/_binary64_2412`
15×	`associate-r_binary64_2405`
14×	`mul-1-neg_binary64_2457`
13×	`distribute-lft-out_binary64_2416`
11×	`unpow3_binary64_2531` `unpow2_binary64_2530` `unpow1_binary64_2523`
10×	`cube-mult_binary64_2495` `associate-l_binary64_2406`
8×	`div-sub_binary64_2470` `distribute-neg-frac_binary64_2429`
7×	`exp-prod_binary64_2517` `distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422`
6×	`cube-div_binary64_2494`
5×	`cube-unmult_binary64_2502` `swap-sqr_binary64_2432`
4×	`log-prod_binary64_2551` `difference-of-sqr--1_binary64_2436` `distribute-lft-neg-out_binary64_2424` `associate-+r-_binary64_2399`
3×	`cube-prod_binary64_2493` `/-rgt-identity_binary64_2456` `associate-*l/_binary64_2408`
2×	`log-div_binary64_2552` `prod-exp_binary64_2514` `exp-diff_binary64_2513` `exp-sum_binary64_2511` `rem-sqrt-square_binary64_2478` `difference-of-sqr-1_binary64_2435` `difference-of-squares_binary64_2434` `distribute-rgt1-in_binary64_2421` `distribute-rgt-out--_binary64_2419`
1×	`unpow1/2_binary64_2529` `pow-plus_binary64_2528` `1-exp_binary64_2509` `rem-square-sqrt_binary64_2477` `*-rgt-identity_binary64_2455` `pow-sqr_binary64_2438` `associate-+l+_binary64_2398`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2728` `erf-erfc_binary64_2727` `erf-odd_binary64_2726` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `not-gte_binary64_2717` `not-lte_binary64_2716` `not-gt_binary64_2715` `not-lt_binary64_2714` `gte-same_binary64_2713` `lte-same_binary64_2712` `gt-same_binary64_2711` `lt-same_binary64_2710` `sinh---cosh_binary64_2657` `sinh-+-cosh_binary64_2656` `sinh-cosh_binary64_2655` `tanh-def-c_binary64_2654` `tanh-def-b_binary64_2653` `tanh-def-a_binary64_2652` `cosh-def_binary64_2651` `sinh-def_binary64_2650` `tan-neg_binary64_2597` `cos-neg_binary64_2596` `sin-neg_binary64_2595` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `hang-m-tan_binary64_2591` `hang-p-tan_binary64_2590` `hang-m0-tan_binary64_2589` `hang-p0-tan_binary64_2588` `hang-0m-tan_binary64_2587` `hang-0p-tan_binary64_2586` `tan-+PI/2_binary64_2585` `tan-+PI_binary64_2584` `tan-PI_binary64_2583` `tan-PI/3_binary64_2582` `tan-PI/4_binary64_2581` `tan-PI/6_binary64_2580` `cos-+PI/2_binary64_2579` `cos-+PI_binary64_2578` `cos-PI_binary64_2577` `cos-PI/2_binary64_2576` `cos-PI/3_binary64_2575` `cos-PI/4_binary64_2574` `cos-PI/6_binary64_2573` `sin-+PI/2_binary64_2572` `sin-+PI_binary64_2571` `sin-PI_binary64_2570` `sin-PI/2_binary64_2569` `sin-PI/3_binary64_2568` `sin-PI/4_binary64_2567` `sin-PI/6_binary64_2566` `sub-1-sin_binary64_2565` `sub-1-cos_binary64_2564` `-1-add-sin_binary64_2563` `-1-add-cos_binary64_2562` `1-sub-sin_binary64_2561` `1-sub-cos_binary64_2560` `cos-sin-sum_binary64_2559` `log-E_binary64_2555` `log-pow_binary64_2554` `log-rec_binary64_2553` `pow-base-0_binary64_2549` `unpow1/3_binary64_2532` `exp-to-pow_binary64_2527` `pow-base-1_binary64_2525` `unpow0_binary64_2524` `unpow-1_binary64_2522` `exp-lft-cube_binary64_2521` `exp-lft-sqr_binary64_2520` `exp-cbrt_binary64_2519` `exp-sqrt_binary64_2518` `div-exp_binary64_2516` `rec-exp_binary64_2515` `exp-neg_binary64_2512` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `rem-log-exp_binary64_2506` `rem-exp-log_binary64_2505` `cube-neg_binary64_2492` `rem-3cbrt-rft_binary64_2491` `rem-3cbrt-lft_binary64_2490` `rem-cbrt-cube_binary64_2489` `rem-cube-cbrt_binary64_2488` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `unsub-neg_binary64_2459` `-lft-identity_binary64_2454` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `mul0-rgt_binary64_2448` `mul0-lft_binary64_2447` `div0_binary64_2446` `-inverses_binary64_2445` `+-inverses_binary64_2444` `lft-mult-inverse_binary64_2443` `rgt-mult-inverse_binary64_2442` `remove-double-div_binary64_2441` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft1-in_binary64_2420` `distribute-lft-out--_binary64_2417` `count-2_binary64_2413` `associate--r-_binary64_2404` `associate--l-_binary64_2403` `associate-+l-_binary64_2400`

Counts

225 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1002	15070
1	3290	14431
2	5003	14431

prune1.2s (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	191	7	198

Error

0.1b

Counts

198 → 7

Compiler

Compiled 17970 to 10546 computations (41.3% saved)

regimes2.6s (7.6%)

Accuracy

Total 1.5b remaining (95.9%)

Threshold costs 0b (0%)

Compiler

Compiled 31940 to 22009 computations (31.1% saved)

bsearch10.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify16.0ms (0%)

Algorithm

1×	egg-herbie

Rules

37×	`+-commutative_binary64_2395`
34×	`*-commutative_binary64_2396`
26×	`sub-neg_binary64_2458`
24×	`neg-mul-1_binary64_2461` `neg-sub0_binary64_2460`
12×	`distribute-rgt-neg-in_binary64_2423` `distribute-lft-neg-in_binary64_2422`
10×	`unsub-neg_binary64_2459` `distribute-neg-in_binary64_2426`
5×	`distribute-neg-frac_binary64_2429`
1×	`1-exp_binary64_2509` `/-rgt-identity_binary64_2456`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_2725` `if-if-and_binary64_2724` `if-if-or-not_binary64_2723` `if-if-or_binary64_2722` `if-not_binary64_2721` `if-same_binary64_2720` `if-false_binary64_2719` `if-true_binary64_2718` `tan-0_binary64_2594` `cos-0_binary64_2593` `sin-0_binary64_2592` `unpow1_binary64_2523` `e-exp-1_binary64_2510` `exp-1-e_binary64_2508` `exp-0_binary64_2507` `sqr-abs_binary64_2480` `sqr-neg_binary64_2479` `mul-1-neg_binary64_2457` `-rgt-identity_binary64_2455` `-lft-identity_binary64_2454` `remove-double-neg_binary64_2453` `sub0-neg_binary64_2452` `--rgt-identity_binary64_2451` `+-rgt-identity_binary64_2450` `+-lft-identity_binary64_2449` `cancel-sign-sub-inv_binary64_2431` `cancel-sign-sub_binary64_2430` `distribute-frac-neg_binary64_2428` `distribute-neg-out_binary64_2427` `distribute-rgt-neg-out_binary64_2425` `distribute-lft-neg-out_binary64_2424`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	185
1	79	185
2	90	185
3	110	185
4	138	185
5	171	185
6	207	185
7	242	185
8	262	185
9	271	185
10	273	185
11	272	185

end0.0ms (0%)

sample3.7s (11.2%)

Algorithm

1×

intervals

Results

377.0ms	6458×	body	128	valid
182.0ms	8000×	pre	128	true
153.0ms	675×	body	1024	valid
87.0ms	515×	body	512	valid
32.0ms	295×	body	256	valid
16.0ms	57×	body	2048	valid

Compiler

Compiled 4138 to 2824 computations (31.8% saved)

Iter	Nodes	Cost
0	52	185
1	79	185
2	90	185
3	110	185
4	138	185
5	171	185
6	207	185
7	242	185
8	262	185
9	271	185
10	273	185
11	272	185

Iter	Nodes	Cost
0	52	185
1	79	185
2	90	185
3	110	185
4	138	185
5	171	185
6	207	185
7	242	185
8	262	185
9	271	185
10	273	185
11	272	185

Details

analyze324.0ms (1%)

sample41.0ms (0.1%)

simplify78.0ms (0.2%)

prune3.0ms (0%)

localize13.0ms (0%)

rewrite388.0ms (1.2%)

series3.7s (11.2%)

simplify210.0ms (0.6%)

prune643.0ms (1.9%)

localize16.0ms (0%)

rewrite359.0ms (1.1%)

series4.0s (11.9%)

simplify204.0ms (0.6%)

prune570.0ms (1.7%)

localize17.0ms (0.1%)

rewrite468.0ms (1.4%)

series5.8s (17.3%)

simplify264.0ms (0.8%)

prune822.0ms (2.5%)

localize19.0ms (0.1%)

rewrite624.0ms (1.9%)

series7.1s (21.2%)

simplify235.0ms (0.7%)

prune1.2s (3.6%)

regimes2.6s (7.6%)

bsearch10.0ms (0%)

simplify16.0ms (0%)

end0.0ms (0%)

sample3.7s (11.2%)

Profiling

Iter	Nodes	Cost
0	52	185
1	79	185
2	90	185
3	110	185
4	138	185
5	171	185
6	207	185
7	242	185
8	262	185
9	271	185
10	273	185
11	272	185