Details

analyze2.5s (17.4%)

Algorithm

1×

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)

sample152.0ms (1.1%)

Algorithm

1×

intervals

Results

76.0ms	81×	body	1024	valid
25.0ms	124×	body	128	valid
21.0ms	36×	body	512	valid
6.0ms	15×	body	256	valid
3.0ms	17×	body	128	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify241.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune15.0ms (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

14.0b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 F (sin.f64 B))
6.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite73.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_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×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

27.0ms	(.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)
7.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 F (sin.f64 B))

series690.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
211.0ms	(/.f64 x (tan.f64 B))
138.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
93.0ms	(/.f64 F (sin.f64 B))

simplify121.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4933	2525
1	4933	2525

prune277.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Error

0.0b

Counts

129 → 13

Compiler

Compiled 3839 to 1862 computations (51.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite108.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_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` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

35.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
21.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
7.0ms	(/.f64 x (tan.f64 B))

series756.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
225.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
175.0ms	(/.f64 x (tan.f64 B))
116.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4950	3927
1	4950	3927

prune318.0ms (2.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	148	15	163

Error

0.0b

Counts

163 → 15

Compiler

Compiled 4983 to 2669 computations (46.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

27.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
15.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
5.0ms	(/.f64 x (tan.f64 B))

series477.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
127.0ms	(/.f64 x (tan.f64 B))
86.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
73.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4978	2141
1	4978	2141

prune189.0ms (1.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	105	15	120

Error

0.0b

Counts

120 → 15

Compiler

Compiled 3145 to 1706 computations (45.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2)) (sin.f64 B))
0.7b	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
16.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
16.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

rewrite103.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`unpow-prod-down_binary64`
39×	`add-exp-log_binary64`
28×	`sqrt-prod_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`prod-exp_binary64`
16×	`unswap-sqr_binary64`
12×	`pow-to-exp_binary64` `swap-sqr_binary64` `sqr-pow_binary64` `pow-exp_binary64`
11×	`add-cbrt-cube_binary64`
10×	`associate-r_binary64` `associate-l_binary64` `div-exp_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 129

Calls

4 calls:

40.0ms	(/.f64 (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2)) (sin.f64 B))
24.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

series342.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2)) (sin.f64 B))
61.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
48.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
31.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

simplify115.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4969	4119
1	4969	4119

prune368.0ms (2.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	141	15	156

Error

0.0b

Counts

156 → 15

Compiler

Compiled 5240 to 3079 computations (41.2% saved)

regimes824.0ms (5.7%)

Accuracy

Total 0.2b remaining (90.8%)

Threshold costs 0.2b (90.8%)

Compiler

Compiled 6064 to 4644 computations (23.4% saved)

bsearch184.0ms (1.3%)

Steps

Iters	Range		Point
9	5023.748525118053	6615465329.427804	12093.64315099762
6	-7.611871682916345e+25	-8.676863023008837e+24	-8.796746510633933e+24

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	100	95
1	100	95

end0.0ms (0%)

sample6.1s (42.4%)

Algorithm

1×

intervals

Results

1.9s	2282×	body	1024	valid
770.0ms	4036×	body	128	valid
643.0ms	1120×	body	512	valid
208.0ms	559×	body	256	valid
118.0ms	640×	body	128	invalid
20.0ms	131×	body	128	nan
5.0ms	3×	body	2048	valid

Compiler

Compiled 1591 to 1208 computations (24.1% saved)

Details

analyze2.5s (17.4%)

sample152.0ms (1.1%)

simplify241.0ms (1.7%)

prune15.0ms (0.1%)

localize19.0ms (0.1%)

rewrite73.0ms (0.5%)

series690.0ms (4.8%)

simplify121.0ms (0.8%)

prune277.0ms (1.9%)

localize34.0ms (0.2%)

rewrite108.0ms (0.7%)

series756.0ms (5.3%)

simplify137.0ms (1%)

prune318.0ms (2.2%)

localize23.0ms (0.2%)

rewrite64.0ms (0.4%)

series477.0ms (3.3%)

simplify105.0ms (0.7%)

prune189.0ms (1.3%)

localize33.0ms (0.2%)

rewrite103.0ms (0.7%)

series342.0ms (2.4%)

simplify115.0ms (0.8%)

prune368.0ms (2.6%)

regimes824.0ms (5.7%)

bsearch184.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.1s (42.4%)

Profiling