Details

analyze2.0s (11.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample157.0ms (0.9%)

Algorithm

1×

intervals

Results

48.0ms	256×	body	128	valid
40.0ms	273×	body	128	nan
33.0ms	171×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5139	41

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 25.4b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.2b	(/.f64 (.f64 M D) (.f64 d 2))
13.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.9b	(sqrt.f64 (/.f64 d h))
14.2b	(sqrt.f64 (/.f64 d l))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`add-exp-log_binary64`
42×	`prod-exp_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
28×	`add-cbrt-cube_binary64`
26×	`sqrt-prod_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`div-exp_binary64`
13×	`associate-r_binary64`
10×	`cbrt-unprod_binary64` `pow-exp_binary64`
8×	`pow1_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

series338.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
77.0ms	(sqrt.f64 (/.f64 d h))
75.0ms	(sqrt.f64 (/.f64 d l))
40.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5222	2151

prune233.0ms (1.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	108	19	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	19	128

Merged error: 11.6b

Counts

128 → 19

Compiler

Compiled 4650 to 2304 computations (50.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
8.2b	(/.f64 (.f64 M D) (.f64 d 2))
13.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.2b	(sqrt.f64 (/.f64 d l))

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64` `div-exp_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
13×	`sqrt-prod_binary64` `sqrt-div_binary64`
12×	`associate-*r/_binary64`
10×	`pow-exp_binary64`
9×	`frac-times_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 124

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 d l))

series2.1s (11.8%)

Counts

4 → 12

Calls

4 calls:

1.8s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
170.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
67.0ms	(sqrt.f64 (/.f64 d l))
45.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4967	4317
1	4967	4317

prune289.0ms (1.6%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	120	16	136
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	125	30	155

Merged error: 9.1b

Counts

155 → 30

Compiler

Compiled 7090 to 2958 computations (58.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
4.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
8.2b	(/.f64 (.f64 M D) (.f64 d 2))
13.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite73.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
9×	`frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

31.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 h)

series2.5s (14%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
151.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
149.0ms	(cbrt.f64 h)
39.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4989	5004
1	4989	5004

prune296.0ms (1.7%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	1	28	29
Picked	1	0	1
Done	0	0	0
Total	124	34	158

Merged error: 6.9b

Counts

158 → 34

Compiler

Compiled 8162 to 3014 computations (63.1% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
4.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (cbrt.f64 h)))))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
8.2b	(/.f64 (.f64 M D) (.f64 d 2))
13.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite84.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
9×	`frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

40.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (cbrt.f64 h)))))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 h)

series2.5s (14.2%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (.f64 (.f64 (cbrt.f64 (cbrt.f64 h)) (cbrt.f64 (cbrt.f64 h))) (cbrt.f64 (cbrt.f64 h)))))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
172.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
150.0ms	(cbrt.f64 h)
39.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4964	5004
1	4964	5004

prune235.0ms (1.3%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	32	33
Picked	1	0	1
Done	0	0	0
Total	128	34	162

Merged error: 6.8b

Counts

162 → 34

Compiler

Compiled 7455 to 2032 computations (72.7% saved)

regimes639.0ms (3.6%)

Compiler: Compiled 9286 to 6182 computations (33.4% saved)

bsearch186.0ms (1%)

Steps

Iters	Range		Point
9	3.2618961725394236e-07	143.18009611299755	5.518926980455547e-05

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	163
1	130	163

end0.0ms (0%)

sample5.6s (31.3%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.3s	8450×	body	128	nan
936.0ms	4816×	body	128	invalid

Compiler

Compiled 1681 to 1112 computations (33.8% saved)

Details

analyze2.0s (11.1%)

sample157.0ms (0.9%)

simplify41.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite39.0ms (0.2%)

series338.0ms (1.9%)

simplify50.0ms (0.3%)

prune233.0ms (1.3%)

localize25.0ms (0.1%)

rewrite66.0ms (0.4%)

series2.1s (11.8%)

simplify99.0ms (0.6%)

prune289.0ms (1.6%)

localize30.0ms (0.2%)

rewrite73.0ms (0.4%)

series2.5s (14%)

simplify100.0ms (0.6%)

prune296.0ms (1.7%)

localize39.0ms (0.2%)

rewrite84.0ms (0.5%)

series2.5s (14.2%)

simplify101.0ms (0.6%)

prune235.0ms (1.3%)

regimes639.0ms (3.6%)

bsearch186.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.6s (31.3%)

Profiling