Details

analyze1.9s (12.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4785	128
1	4785	128
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample93.0ms (0.6%)

Algorithm

1×

intervals

Results

36.0ms	65×	body	1024	valid
18.0ms	142×	body	128	valid
14.0ms	37×	body	512	valid
3.0ms	12×	body	256	valid
2.0ms	20×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify143.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.3b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
8.8b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
19.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite229.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

11.2b

Rules

44×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`prod-exp_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series866.0ms (5.7%)

Error

0.1b

Counts

4 → 40

Calls

4 calls:

330.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
214.0ms	(/.f64 x (tan.f64 B))
165.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
105.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3157 to 2279 computations (27.8% saved)

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5001	3014

prune222.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	142	13	155
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Error

0.0b

Counts

157 → 13

Compiler

Compiled 4478 to 2154 computations (51.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
19.4b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite255.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
25×	`unpow-prod-down_binary64` `associate-r_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`pow-pow_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4662 to 2467 computations (47.1% saved)

series1.0s (6.7%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

321.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
304.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
198.0ms	(/.f64 x (tan.f64 B))
144.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

Compiler

Compiled 3659 to 2683 computations (26.7% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4965	4578
1	4965	4578

prune256.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	183	13	196

Error

0.0b

Counts

196 → 13

Compiler

Compiled 5666 to 2984 computations (47.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (/.f64 1 (sin.f64 B))))
0.4b	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 1 (sin.f64 B)))
19.4b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite242.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

67×	`add-exp-log_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`prod-exp_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64` `times-frac_binary64`
20×	`add-cbrt-cube_binary64`
14×	`associate-r_binary64`
13×	`div-exp_binary64`
10×	`associate-l_binary64`
9×	`unpow-prod-down_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unswap-sqr_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64`
6×	`1-exp_binary64` `rec-exp_binary64`
5×	`sqr-pow_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`un-div-inv_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`pow-pow_binary64` `pow-prod-down_binary64` `frac-2neg_binary64` `clear-num_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 129

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 1 (sin.f64 B)))
13.0ms	(.f64 F (.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (/.f64 1 (sin.f64 B))))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4204 to 2354 computations (44% saved)

series952.0ms (6.3%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

298.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 1 (sin.f64 B)))
297.0ms	(.f64 F (.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (/.f64 1 (sin.f64 B))))
177.0ms	(/.f64 x (tan.f64 B))
130.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

Compiler

Compiled 3751 to 2775 computations (26% saved)

simplify94.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4927	3869
1	4927	3869

prune228.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	174	13	187

Error

0.0b

Counts

187 → 13

Compiler

Compiled 4997 to 2719 computations (45.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
8.8b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
19.4b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
19.4b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

rewrite460.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`add-exp-log_binary64`
58×	`add-sqr-sqrt_binary64`
47×	`prod-exp_binary64`
44×	`unpow-prod-down_binary64`
28×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
23×	`associate-l_binary64`
18×	`add-cbrt-cube_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unswap-sqr_binary64`
12×	`sqr-pow_binary64` `swap-sqr_binary64`
11×	`associate-r_binary64`
10×	`div-exp_binary64` `times-frac_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `*-commutative_binary64`
1×	`associate-*l/_binary64` `div-inv_binary64` `pow2_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`

Counts

4 → 150

Calls

4 calls:

22.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
22.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
6.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
5.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

Compiler

Compiled 7593 to 4488 computations (40.9% saved)

series690.0ms (4.5%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

315.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
111.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
105.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
104.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))

Compiler

Compiled 4115 to 2989 computations (27.4% saved)

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4945	5263
1	4945	5263

prune314.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	196	12	208

Error

0.0b

Counts

208 → 12

Compiler

Compiled 6653 to 3590 computations (46% saved)

regimes1.2s (8%)

Accuracy

Total 0.2b remaining (90.9%)

Threshold costs 0.2b (90.9%)

Compiler

Compiled 12192 to 9256 computations (24.1% saved)

bsearch157.0ms (1%)

Steps

Iters	Range		Point
11	16506.084420278352	1.59868228236987e+31	111983907.8550106
7	-2868339705733.0703	-16665083368.323484	-18621346198.865578

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	71
1	53	71

end0.0ms (0%)

sample5.5s (36.1%)

Algorithm

1×

intervals

Results

1.3s	2273×	body	1024	valid
534.0ms	4082×	body	128	valid
420.0ms	1090×	body	512	valid
144.0ms	552×	body	256	valid
85.0ms	690×	body	128	invalid
12.0ms	122×	body	128	nan
3.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 3107 to 2353 computations (24.3% saved)

Details

analyze1.9s (12.7%)

sample93.0ms (0.6%)

simplify143.0ms (0.9%)

prune9.0ms (0.1%)

localize18.0ms (0.1%)

rewrite229.0ms (1.5%)

series866.0ms (5.7%)

simplify73.0ms (0.5%)

prune222.0ms (1.5%)

localize20.0ms (0.1%)

rewrite255.0ms (1.7%)

series1.0s (6.7%)

simplify83.0ms (0.5%)

prune256.0ms (1.7%)

localize21.0ms (0.1%)

rewrite242.0ms (1.6%)

series952.0ms (6.3%)

simplify94.0ms (0.6%)

prune228.0ms (1.5%)

localize19.0ms (0.1%)

rewrite460.0ms (3%)

series690.0ms (4.5%)

simplify96.0ms (0.6%)

prune314.0ms (2.1%)

regimes1.2s (8%)

bsearch157.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.5s (36.1%)

Profiling