Details

analyze1.9s (17.9%)

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)

sample117.0ms (1.1%)

Algorithm

1×

intervals

Results

44.0ms	58×	body	1024	valid
25.0ms	133×	body	128	valid
23.0ms	47×	body	512	valid
6.0ms	18×	body	256	valid
3.0ms	23×	body	128	invalid
1.0ms	1×	body	1024	invalid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify287.0ms (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: 13.9b

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))
6.0b	(.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)

rewrite45.0ms (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:

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

series757.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

284.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
236.0ms	(/.f64 x (tan.f64 B))
134.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
103.0ms	(/.f64 F (sin.f64 B))

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4913	2519
1	4913	2519

prune219.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	12	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

Compiler

Compiled 3841 to 1852 computations (51.8% saved)

localize22.0ms (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)

rewrite55.0ms (0.5%)

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:

16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(/.f64 (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))

series827.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
242.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
201.0ms	(/.f64 x (tan.f64 B))
124.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4937	3927
1	4937	3927

prune242.0ms (2.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	148	14	162

Merged error: 0.0b

Counts

162 → 14

Compiler

Compiled 4981 to 2656 computations (46.7% saved)

localize20.0ms (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))
6.0b	(.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)

rewrite47.0ms (0.4%)

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))

series623.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

273.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
147.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
118.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
85.0ms	(/.f64 x (sin.f64 B))

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (61.0ms)

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	1	11	12
Picked	0	1	1
Done	0	1	1
Total	131	14	145

Merged error: 0.0b

Counts

145 → 14

Compiler

Compiled 4349 to 1930 computations (55.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
6.0b	(.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)

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
15×	`times-frac_binary64`
10×	`associate-r_binary64`
8×	`unpow-prod-down_binary64` `prod-exp_binary64`
7×	`pow1_binary64` `unswap-sqr_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` `pow-exp_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `associate-l/_binary64`

Counts

4 → 99

Calls

4 calls:

19.0ms	(.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)
5.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))

series608.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

283.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
156.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
120.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
48.0ms	(*.f64 x (cos.f64 B))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4916	2293
1	4916	2293

prune140.0ms (1.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	111	14	125

Merged error: 0.0b

Counts

125 → 14

Compiler

Compiled 3361 to 1454 computations (56.7% saved)

regimes131.0ms (1.2%)

Compiler: Compiled 1062 to 807 computations (24% saved)

bsearch172.0ms (1.6%)

Steps

Iters	Range		Point
9	1.7243352283322197	56857968.78426548	431818.2464669147
9	-3.4833683282504698e+25	-1.66429097932421e+17	-2.0144658748720362e+17

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	100
1	96	100

end0.0ms (0%)

sample3.7s (35.3%)

Algorithm

1×

intervals

Results

1.6s	2143×	body	1024	valid
611.0ms	4207×	body	128	valid
527.0ms	1121×	body	512	valid
164.0ms	527×	body	256	valid
104.0ms	707×	body	128	invalid
12.0ms	115×	body	128	nan
3.0ms	2×	body	2048	valid
2.0ms	3×	body	1024	invalid

Compiler

Compiled 445 to 326 computations (26.7% saved)

Details

analyze1.9s (17.9%)

sample117.0ms (1.1%)

simplify287.0ms (2.7%)

prune9.0ms (0.1%)

localize21.0ms (0.2%)

rewrite45.0ms (0.4%)

series757.0ms (7.2%)

simplify100.0ms (0.9%)

prune219.0ms (2.1%)

localize22.0ms (0.2%)

rewrite55.0ms (0.5%)

series827.0ms (7.8%)

simplify85.0ms (0.8%)

prune242.0ms (2.3%)

localize20.0ms (0.2%)

rewrite47.0ms (0.4%)

series623.0ms (5.9%)

simplify88.0ms (0.8%)

prune179.0ms (1.7%)

localize20.0ms (0.2%)

rewrite47.0ms (0.4%)

series608.0ms (5.7%)

simplify86.0ms (0.8%)

prune140.0ms (1.3%)

regimes131.0ms (1.2%)

bsearch172.0ms (1.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.7s (35.3%)

Profiling