Details

analyze1.9s (18.4%)

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)

sample121.0ms (1.1%)

Algorithm

1×

intervals

Results

50.0ms	66×	body	1024	valid
23.0ms	130×	body	128	valid
21.0ms	41×	body	512	valid
6.0ms	18×	body	256	valid
4.0ms	25×	body	128	invalid
2.0ms	1×	body	2048	valid
1.0ms	5×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify286.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5147	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

Merged error: 11.6b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
6.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite46.0ms (0.4%)

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:

16.0ms	(.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)
4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

series748.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
224.0ms	(/.f64 x (tan.f64 B))
136.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
103.0ms	(/.f64 F (sin.f64 B))

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4913	2519
1	4913	2519

prune201.0ms (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

Merged error: 0.0b

Counts

129 → 13

Compiler

Compiled 3879 to 1884 computations (51.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.4b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms (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:

12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series701.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
207.0ms	(/.f64 x (tan.f64 B))
117.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
91.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5034	2141

prune145.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 3161 to 1709 computations (45.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
6.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 x (sin.f64 B))

series652.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
163.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
117.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
91.0ms	(/.f64 x (sin.f64 B))

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4918	2635
1	4918	2635

prune179.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	130	14	144

Merged error: 0b

Counts

144 → 14

Compiler

Compiled 4373 to 1949 computations (55.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 B) x)
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
6.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
11×	`div-exp_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64` `div-inv_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
4.0ms	(/.f64 (tan.f64 B) x)

series653.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
168.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
115.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
95.0ms	(/.f64 (tan.f64 B) x)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4900	3440
1	4900	3440

prune225.0ms (2.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	176	14	190

Merged error: 0b

Counts

190 → 14

Compiler

Compiled 5244 to 2486 computations (52.6% saved)

regimes130.0ms (1.2%)

Compiler: Compiled 1134 to 864 computations (23.8% saved)

bsearch151.0ms (1.4%)

Steps

Iters	Range		Point
9	1967.1600101361114	1848276683.7893198	10961.56718343877
7	-1.916304669298546e+20	-1.0355547609179217e+18	-5.1418416781795934e+19

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	67	90
1	67	90

end0.0ms (0%)

sample3.8s (35.7%)

Algorithm

1×

intervals

Results

1.7s	2249×	body	1024	valid
619.0ms	4129×	body	128	valid
505.0ms	1070×	body	512	valid
172.0ms	545×	body	256	valid
100.0ms	651×	body	128	invalid
13.0ms	120×	body	128	nan
9.0ms	7×	body	2048	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 463 to 344 computations (25.7% saved)

Details

analyze1.9s (18.4%)

sample121.0ms (1.1%)

simplify286.0ms (2.7%)

prune9.0ms (0.1%)

localize21.0ms (0.2%)

rewrite46.0ms (0.4%)

series748.0ms (7.1%)

simplify92.0ms (0.9%)

prune201.0ms (1.9%)

localize22.0ms (0.2%)

rewrite46.0ms (0.4%)

series701.0ms (6.6%)

simplify59.0ms (0.6%)

prune145.0ms (1.4%)

localize21.0ms (0.2%)

rewrite48.0ms (0.5%)

series652.0ms (6.2%)

simplify88.0ms (0.8%)

prune179.0ms (1.7%)

localize24.0ms (0.2%)

rewrite53.0ms (0.5%)

series653.0ms (6.2%)

simplify128.0ms (1.2%)

prune225.0ms (2.1%)

regimes130.0ms (1.2%)

bsearch151.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.8s (35.7%)

Profiling