Details

analyze288.0ms (3.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample34.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	245×	body	128	valid
9.0ms	286×	pre	128	true
1.0ms	30×	body	128	nan
1.0ms	11×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify361.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 3 a) c)
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
28.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2487`
14×	`*-un-lft-identity_binary64_2465` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`pow1_binary64_2526`
8×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500`
6×	`difference-of-squares_binary64_2434` `times-frac_binary64_2471` `associate-/l*_binary64_2410`
4×	`cancel-sign-sub-inv_binary64_2431` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
3×	`sqrt-prod_binary64_2481` `flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `associate-r_binary64_2405` `pow-prod-down_binary64_2536` `flip3--_binary64_2469`
2×	`associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `diff-log_binary64_2557`
1×	`-commutative_binary64_2396` `associate-/r_binary64_2409` `clear-num_binary64_2464` `div-sub_binary64_2470` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `associate-l_binary64_2406`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series251.0ms (3.2%)

Counts

4 → 33

Calls

4 calls:

114.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
72.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
36.0ms	(.f64 (.f64 3 a) c)
28.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5232	2392

prune145.0ms (1.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	93	17	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	17	111

Merged error: 2.9b

Counts

111 → 17

Compiler

Compiled 2958 to 1753 computations (40.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
0.2b	(.f64 a (.f64 c c))
0.3b	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
0.4b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64_2503`
32×	`add-cbrt-cube_binary64_2501`
31×	`prod-exp_binary64_2514`
24×	`times-frac_binary64_2471`
19×	`add-sqr-sqrt_binary64_2487` `associate-l_binary64_2406`
18×	`div-exp_binary64_2516`
16×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
13×	`cbrt-unprod_binary64_2498`
12×	`associate-/r*_binary64_2409`
11×	`pow1_binary64_2526`
9×	`cube-prod_binary64_2493` `unpow-prod-down_binary64_2544`
6×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534`
4×	`associate-r_binary64_2405` `pow-prod-down_binary64_2536`
3×	`associate-*l/_binary64_2408` `unpow3_binary64_2531` `cube-mult_binary64_2495` `sqr-pow_binary64_2437`
2×	`*-commutative_binary64_2396` `unswap-sqr_binary64_2433` `div-inv_binary64_2462`
1×	`flip3-+_binary64_2468` `+-commutative_binary64_2395` `sum-log_binary64_2556` `flip-+_binary64_2439` `clear-num_binary64_2464` `frac-2neg_binary64_2476` `associate-/l*_binary64_2410` `frac-add_binary64_2473`

Counts

4 → 122

Calls

4 calls:

14.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
10.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
8.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
6.0ms	(.f64 a (.f64 c c))

series460.0ms (5.9%)

Counts

4 → 33

Calls

4 calls:

180.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
167.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
71.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
41.0ms	(.f64 a (.f64 c c))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5158	2520

prune182.0ms (2.3%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	148	24	172

Merged error: 2.9b

Counts

172 → 24

Compiler

Compiled 3891 to 2092 computations (46.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 a (.f64 c c))
0.3b	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
0.3b	(.f64 (.f64 a (*.f64 c c)) -3/8)
0.3b	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64_2503`
34×	`add-cbrt-cube_binary64_2501`
32×	`pow1_binary64_2526`
24×	`add-sqr-sqrt_binary64_2487`
23×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
21×	`times-frac_binary64_2471`
19×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
12×	`unpow-prod-down_binary64_2544`
7×	`associate-/r_binary64_2409` `associate-l*_binary64_2406`
5×	`associate-r_binary64_2405`
4×	`add-log-exp_binary64_2504` `sqr-pow_binary64_2437`
3×	`-commutative_binary64_2396` `div-exp_binary64_2516` `associate-/l_binary64_2410`
2×	`associate-/l/_binary64_2412`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `unswap-sqr_binary64_2433` `pow-to-exp_binary64_2534` `div-inv_binary64_2462` `frac-2neg_binary64_2476`

Counts

4 → 111

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))
11.0ms	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
8.0ms	(.f64 (.f64 a (*.f64 c c)) -3/8)
6.0ms	(.f64 a (.f64 c c))

series302.0ms (3.9%)

Counts

4 → 30

Calls

4 calls:

119.0ms	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
91.0ms	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))
54.0ms	(.f64 (.f64 a (*.f64 c c)) -3/8)
38.0ms	(.f64 a (.f64 c c))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	3505

prune244.0ms (3.1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	132	9	141
Fresh	3	19	22
Picked	1	0	1
Done	0	1	1
Total	136	29	165

Merged error: 2.8b

Counts

165 → 29

Compiler

Compiled 4908 to 2995 computations (39% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
0.3b	(/.f64 (-.f64 (.f64 (/.f64 (.f64 c c) (.f64 b b)) 1/4) (.f64 (/.f64 a (/.f64 (pow.f64 b 6) (.f64 (pow.f64 c 4) a))) 9/64)) (-.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)))
0.4b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
0.4b	(/.f64 (pow.f64 b 6) (*.f64 (pow.f64 c 4) a))

rewrite77.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-exp-log_binary64_2503`
40×	`times-frac_binary64_2471`
37×	`prod-exp_binary64_2514`
34×	`add-cbrt-cube_binary64_2501`
31×	`div-exp_binary64_2516`
29×	`add-sqr-sqrt_binary64_2487`
27×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
16×	`associate-/r_binary64_2409` `associate-l*_binary64_2406`
15×	`unpow-prod-down_binary64_2544`
13×	`pow-exp_binary64_2533` `pow-to-exp_binary64_2534`
11×	`associate-/l*_binary64_2410` `cbrt-unprod_binary64_2498`
9×	`cube-prod_binary64_2493` `cbrt-undiv_binary64_2499`
6×	`pow1_binary64_2526`
5×	`associate-*l/_binary64_2408` `sqr-pow_binary64_2437`
4×	`add-log-exp_binary64_2504` `div-inv_binary64_2462`
3×	`unpow3_binary64_2531` `associate-/l/_binary64_2412` `clear-num_binary64_2464` `cube-mult_binary64_2495` `associate-/r/_binary64_2411` `frac-2neg_binary64_2476` `associate-r_binary64_2405`
2×	`flip--_binary64_2440` `flip3--_binary64_2469` `frac-sub_binary64_2474`
1×	`*-commutative_binary64_2396` `div-sub_binary64_2470` `unswap-sqr_binary64_2433` `pow-prod-down_binary64_2536`

Counts

4 → 164

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (.f64 (/.f64 (.f64 c c) (.f64 b b)) 1/4) (.f64 (/.f64 a (/.f64 (pow.f64 b 6) (.f64 (pow.f64 c 4) a))) 9/64)) (-.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)))
17.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
9.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
7.0ms	(/.f64 (pow.f64 b 6) (*.f64 (pow.f64 c 4) a))

series748.0ms (9.6%)

Counts

4 → 36

Calls

4 calls:

231.0ms	(/.f64 (pow.f64 b 6) (*.f64 (pow.f64 c 4) a))
193.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
169.0ms	(/.f64 (-.f64 (.f64 (/.f64 (.f64 c c) (.f64 b b)) 1/4) (.f64 (/.f64 a (/.f64 (pow.f64 b 6) (.f64 (pow.f64 c 4) a))) 9/64)) (-.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)))
155.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5149	5356

prune459.0ms (5.9%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	195	5	200
Fresh	5	22	27
Picked	1	0	1
Done	0	1	1
Total	201	28	229

Merged error: 2.7b

Counts

229 → 28

Compiler

Compiled 9376 to 5059 computations (46% saved)

regimes1.0s (13%)

Compiler: Compiled 11588 to 8302 computations (28.4% saved)

bsearch4.0ms (0.1%)

Steps

Iters	Range		Point
0	4.228478054994806	4.278618149550354	4.25354810227258

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	179	116
1	179	116

end0.0ms (0%)

sample2.7s (34.9%)

Algorithm

1×

intervals

Results

407.0ms	7689×	body	128	valid
289.0ms	9028×	pre	128	true
51.0ms	1028×	body	128	nan
31.0ms	311×	body	256	valid

Compiler

Compiled 2333 to 1664 computations (28.7% saved)

Details

analyze288.0ms (3.7%)

sample34.0ms (0.4%)

simplify361.0ms (4.6%)

prune4.0ms (0%)

localize13.0ms (0.2%)

rewrite36.0ms (0.5%)

series251.0ms (3.2%)

simplify52.0ms (0.7%)

prune145.0ms (1.9%)

localize16.0ms (0.2%)

rewrite48.0ms (0.6%)

series460.0ms (5.9%)

simplify74.0ms (1%)

prune182.0ms (2.3%)

localize16.0ms (0.2%)

rewrite52.0ms (0.7%)

series302.0ms (3.9%)

simplify76.0ms (1%)

prune244.0ms (3.1%)

localize27.0ms (0.3%)

rewrite77.0ms (1%)

series748.0ms (9.6%)

simplify103.0ms (1.3%)

prune459.0ms (5.9%)

regimes1.0s (13%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.7s (34.9%)

Profiling