Details

analyze1.9s (16.7%)

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)

sample112.0ms (1%)

Algorithm

1×

intervals

Results

42.0ms	55×	body	1024	valid
25.0ms	49×	body	512	valid
21.0ms	138×	body	128	valid
4.0ms	14×	body	256	valid
4.0ms	28×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify316.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5787	32

prune11.0ms (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: 15.9b

Counts

2 → 2

Compiler

Compiled 117 to 97 computations (17.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
8.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite54.0ms (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:

17.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
16.0ms	(.f64 (/.f64 F (sin.f64 B)) (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))

series747.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

295.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
227.0ms	(/.f64 x (tan.f64 B))
122.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
102.0ms	(/.f64 F (sin.f64 B))

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4930	2525
1	4930	2525

prune876.0ms (7.6%)

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 16590 to 11368 computations (31.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
18.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite47.0ms (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))

series675.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

268.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
205.0ms	(/.f64 x (tan.f64 B))
109.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
92.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5181	2141

prune252.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

Compiler

Compiled 5136 to 3166 computations (38.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
0.6b	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
18.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
26×	`div-exp_binary64`
20×	`add-cbrt-cube_binary64`
15×	`prod-exp_binary64`
8×	`associate-/r*_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64`
6×	`pow-to-exp_binary64` `pow1_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-exp_binary64`
5×	`1-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 127

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
13.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (sin.f64 B) (.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)

series825.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

332.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
278.0ms	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
111.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
104.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4926	3733
1	4926	3733

prune216.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	139	12	151

Merged error: 0.0b

Counts

151 → 12

Compiler

Compiled 4626 to 2661 computations (42.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(*.f64 x (/.f64 1 (tan.f64 B)))
8.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64` `times-frac_binary64`
31×	`add-cube-cbrt_binary64`
29×	`add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
10×	`prod-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`unpow-prod-down_binary64`
7×	`pow1_binary64`
6×	`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×	`*-commutative_binary64`
1×	`pow-prod-down_binary64` `1-exp_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `un-div-inv_binary64` `tan-quot_binary64` `associate-l/_binary64`

Counts

4 → 124

Calls

4 calls:

16.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
9.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
4.0ms	(/.f64 F (sin.f64 B))

series705.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
219.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
115.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
89.0ms	(/.f64 F (sin.f64 B))

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4901	2540
1	4901	2540

prune245.0ms (2.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	136	12	148

Merged error: 0.0b

Counts

148 → 12

Compiler

Compiled 5280 to 3038 computations (42.5% saved)

regimes112.0ms (1%)

Compiler: Compiled 933 to 705 computations (24.4% saved)

bsearch154.0ms (1.3%)

Steps

Iters	Range		Point
8	15724029.99783543	51231343519.1465	111746443.95311779
8	-1.621079407319948e+17	-4286670999119.038	-6391356515907.039

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	82	96
1	82	96

end0.0ms (0%)

sample3.7s (32%)

Algorithm

1×

intervals

Results

1.6s	2163×	body	1024	valid
614.0ms	4112×	body	128	valid
555.0ms	1149×	body	512	valid
182.0ms	574×	body	256	valid
101.0ms	674×	body	128	invalid
14.0ms	136×	body	128	nan
3.0ms	2×	body	2048	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 400 to 295 computations (26.3% saved)

Details

analyze1.9s (16.7%)

sample112.0ms (1%)

simplify316.0ms (2.7%)

prune11.0ms (0.1%)

localize21.0ms (0.2%)

rewrite54.0ms (0.5%)

series747.0ms (6.5%)

simplify93.0ms (0.8%)

prune876.0ms (7.6%)

localize22.0ms (0.2%)

rewrite47.0ms (0.4%)

series675.0ms (5.9%)

simplify60.0ms (0.5%)

prune252.0ms (2.2%)

localize20.0ms (0.2%)

rewrite65.0ms (0.6%)

series825.0ms (7.2%)

simplify90.0ms (0.8%)

prune216.0ms (1.9%)

localize21.0ms (0.2%)

rewrite53.0ms (0.5%)

series705.0ms (6.1%)

simplify119.0ms (1%)

prune245.0ms (2.1%)

regimes112.0ms (1%)

bsearch154.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.7s (32%)

Profiling