Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	pre	128	true
7.0ms	189×	body	128	valid
4.0ms	35×	body	1024	valid
2.0ms	22×	body	512	valid
1.0ms	3×	body	2048	valid
0.0ms	7×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify286.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4878	19
1	4878	19

prune2.0ms (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

Merged error: 16.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2436`
26×	`add-sqr-sqrt_binary64_2457`
25×	`times-frac_binary64_2442`
19×	`distribute-lft-out_binary64_2389`
14×	`add-cube-cbrt_binary64_2468`
6×	`distribute-lft-out--_binary64_2390` `difference-of-squares_binary64_2405`
5×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
4×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `pow1_binary64_2494` `div-sub_binary64_2441` `associate-/l/_binary64_2385`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `associate-+l-_binary64_2373` `div-exp_binary64_2484` `flip3--_binary64_2440` `sum-log_binary64_2524` `clear-num_binary64_2435` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `flip--_binary64_2411`

Counts

2 → 65

Calls

2 calls:

23.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series156.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

91.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
64.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5354	1488

prune94.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 16.1b

Counts

72 → 11

Compiler

Compiled 1727 to 977 computations (43.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite89.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_2436`
67×	`add-sqr-sqrt_binary64_2457`
58×	`times-frac_binary64_2442`
36×	`add-cube-cbrt_binary64_2468`
24×	`distribute-lft-out_binary64_2389`
13×	`distribute-lft-out--_binary64_2390` `associate-/l_binary64_2383` `associate-/r_binary64_2382`
12×	`difference-of-squares_binary64_2405`
10×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
6×	`add-log-exp_binary64_2472`
4×	`associate-/r/_binary64_2384` `pow1_binary64_2494` `associate-/l/_binary64_2385`
3×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `div-exp_binary64_2484` `flip3--_binary64_2440` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `flip--_binary64_2411`
2×	`flip3-+_binary64_2439` `frac-sub_binary64_2445` `flip-+_binary64_2410` `difference-of-sqr-1_binary64_2406`
1×	`diff-log_binary64_2525` `div-sub_binary64_2441` `sub-neg_binary64_2429`

Counts

4 → 140

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
9.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series317.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
94.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
71.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
53.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5297	3801

prune235.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	156	7	163

Merged error: 2.9b

Counts

163 → 7

Compiler

Compiled 4527 to 2737 computations (39.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.4b	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.5b	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite109.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_2436`
125×	`add-sqr-sqrt_binary64_2457`
121×	`times-frac_binary64_2442`
81×	`sqrt-prod_binary64_2451`
68×	`add-cube-cbrt_binary64_2468`
42×	`distribute-lft-out_binary64_2389`
32×	`add-exp-log_binary64_2471`
30×	`associate-r_binary64_2378` `associate-l_binary64_2379`
20×	`add-cbrt-cube_binary64_2469`
16×	`associate-/r*_binary64_2382`
15×	`unswap-sqr_binary64_2404`
11×	`div-exp_binary64_2484`
8×	`prod-exp_binary64_2482` `associate-/r/_binary64_2384` `pow1_binary64_2494` `sqrt-div_binary64_2452`
6×	`cbrt-undiv_binary64_2467` `associate-/l*_binary64_2383` `add-log-exp_binary64_2472`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `div-inv_binary64_2433` `cbrt-unprod_binary64_2466` `difference-of-squares_binary64_2405`
3×	`rec-exp_binary64_2483` `1-exp_binary64_2477` `pow-flip_binary64_2507`
2×	`clear-num_binary64_2435` `frac-2neg_binary64_2447` `difference-of-sqr-1_binary64_2406`
1×	`distribute-lft-out--_binary64_2390` `-commutative_binary64_2369` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `inv-pow_binary64_2518` `pow1/2_binary64_2513` `flip3--_binary64_2440` `associate-r/_binary64_2380` `associate-*l/_binary64_2381` `frac-times_binary64_2446` `flip--_binary64_2411` `sqrt-pow1_binary64_2453` `sub-neg_binary64_2429`

Counts

4 → 221

Calls

4 calls:

38.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
10.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

series376.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
101.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
91.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
69.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))

simplify108.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4960	4829
1	4960	4829

prune430.0ms (7.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	229	4	233
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	232	8	240

Merged error: 2.9b

Counts

240 → 8

Compiler

Compiled 8456 to 5324 computations (37% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.6b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
11.0b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite123.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`*-un-lft-identity_binary64_2436`
78×	`add-sqr-sqrt_binary64_2457`
66×	`times-frac_binary64_2442`
50×	`log-prod_binary64_2519`
37×	`add-cube-cbrt_binary64_2468`
25×	`exp-sum_binary64_2479`
19×	`distribute-lft-out--_binary64_2390`
16×	`difference-of-squares_binary64_2405`
12×	`distribute-lft-out_binary64_2389`
9×	`add-exp-log_binary64_2471`
6×	`add-log-exp_binary64_2472` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
5×	`associate-/r*_binary64_2382`
4×	`exp-prod_binary64_2485`
3×	`div-inv_binary64_2433` `associate-/l*_binary64_2383`
2×	`log-pow_binary64_2522` `associate-/r/_binary64_2384` `div-exp_binary64_2484` `log-div_binary64_2520` `difference-of-sqr-1_binary64_2406` `rem-log-exp_binary64_2474`
1×	`flip3-+_binary64_2439` `cbrt-undiv_binary64_2467` `exp-diff_binary64_2481` `flip-+_binary64_2410` `diff-log_binary64_2525` `flip3--_binary64_2440` `clear-num_binary64_2435` `rem-exp-log_binary64_2473` `frac-2neg_binary64_2447` `flip--_binary64_2411` `sub-neg_binary64_2429`

Counts

4 → 129

Calls

4 calls:

40.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
37.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series542.0ms (9%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
179.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
86.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
53.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify124.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4869	4513
1	4869	4513

prune216.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Merged error: 2.9b

Counts

149 → 11

Compiler

Compiled 4281 to 2720 computations (36.5% saved)

regimes605.0ms (10%)

Compiler: Compiled 7855 to 5812 computations (26% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	226	86
1	226	86

end0.0ms (0%)

sample2.0s (32.4%)

Algorithm

1×

intervals

Results

205.0ms	5968×	body	128	valid
138.0ms	8000×	pre	128	true
130.0ms	1019×	body	1024	valid
59.0ms	601×	body	512	valid
22.0ms	307×	body	256	valid
17.0ms	105×	body	2048	valid

Compiler

Compiled 1635 to 1208 computations (26.1% saved)

Details

analyze3.0ms (0.1%)

sample31.0ms (0.5%)

simplify286.0ms (4.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite40.0ms (0.7%)

series156.0ms (2.6%)

simplify68.0ms (1.1%)

prune94.0ms (1.5%)

localize12.0ms (0.2%)

rewrite89.0ms (1.5%)

series317.0ms (5.2%)

simplify75.0ms (1.2%)

prune235.0ms (3.9%)

localize18.0ms (0.3%)

rewrite109.0ms (1.8%)

series376.0ms (6.2%)

simplify108.0ms (1.8%)

prune430.0ms (7.1%)

localize13.0ms (0.2%)

rewrite123.0ms (2%)

series542.0ms (9%)

simplify124.0ms (2.1%)

prune216.0ms (3.6%)

regimes605.0ms (10%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (32.4%)

Profiling