Details

analyze1.3s (13.2%)

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%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 18 to 17 computations (5.6% saved)

sample87.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
22.0ms	209×	body	128	invalid
13.0ms	151×	body	128	nan

Compiler

Compiled 35 to 37 computations (-5.7% saved)

simplify308.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	4864	25
1	4864	25

prune9.0ms (0.1%)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 32 to 30 computations (6.3% saved)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.0b	(sqrt.f64 (exp.f64 t))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_14097`
14×	`associate-r_binary64_13999`
13×	`add-sqr-sqrt_binary64_14081`
10×	`add-cbrt-cube_binary64_14095` `add-cube-cbrt_binary64_14094` `prod-exp_binary64_14108` `*-un-lft-identity_binary64_14059`
7×	`sqrt-prod_binary64_14075`
6×	`associate-*l/_binary64_14002` `unpow-prod-down_binary64_14138` `pow1_binary64_14120`
4×	`cbrt-unprod_binary64_14092` `sqrt-pow1_binary64_14077` `associate-l_binary64_14000`
3×	`add-log-exp_binary64_14098` `exp-prod_binary64_14111`
2×	`flip--_binary64_14034` `*-commutative_binary64_13990` `pow-exp_binary64_14127` `pow-to-exp_binary64_14128` `flip3--_binary64_14063`
1×	`rem-sqrt-square_binary64_14072` `sqr-pow_binary64_14031` `pow1/2_binary64_14139` `unswap-sqr_binary64_14027` `pow-prod-down_binary64_14130`

Counts

3 → 66

Calls

3 calls:

15.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
10.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
3.0ms	(sqrt.f64 (exp.f64 t))

series498.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

386.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
87.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
25.0ms	(sqrt.f64 (exp.f64 t))

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4981	1443
1	4981	1443

prune139.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Error

0.0b

Counts

76 → 8

Compiler

Compiled 1811 to 1063 computations (41.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.0b	(sqrt.f64 (exp.f64 t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.4b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64_14097`
22×	`associate-r_binary64_13999` `prod-exp_binary64_14108`
20×	`add-cbrt-cube_binary64_14095`
19×	`add-sqr-sqrt_binary64_14081`
14×	`add-cube-cbrt_binary64_14094` `*-un-lft-identity_binary64_14059`
13×	`sqrt-prod_binary64_14075`
12×	`associate-*l/_binary64_14002` `pow1_binary64_14120`
10×	`cbrt-unprod_binary64_14092`
6×	`unpow-prod-down_binary64_14138`
5×	`associate-l_binary64_14000`
4×	`add-log-exp_binary64_14098` `pow-prod-down_binary64_14130` `sqrt-pow1_binary64_14077`
3×	`flip--_binary64_14034` `*-commutative_binary64_13990` `exp-prod_binary64_14111` `pow-exp_binary64_14127` `pow-to-exp_binary64_14128` `flip3--_binary64_14063`
2×	`unswap-sqr_binary64_14027`
1×	`rem-sqrt-square_binary64_14072` `sqr-pow_binary64_14031` `pow1/2_binary64_14139`

Counts

4 → 96

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
10.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
2.0ms	(sqrt.f64 (exp.f64 t))

series632.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

425.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
132.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
60.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
15.0ms	(sqrt.f64 (exp.f64 t))

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4966	2102
1	4966	2102

prune169.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Error

0.0b

Counts

116 → 8

Compiler

Compiled 2578 to 1419 computations (45% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))
0.1b	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))

rewrite71.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64_14075`
19×	`pow1_binary64_14120`
17×	`add-sqr-sqrt_binary64_14081`
14×	`associate-r_binary64_13999`
12×	`sqrt-pow1_binary64_14077`
11×	`add-cbrt-cube_binary64_14095` `add-cube-cbrt_binary64_14094` `*-un-lft-identity_binary64_14059` `add-exp-log_binary64_14097`
6×	`associate-*l/_binary64_14002` `pow-prod-down_binary64_14130`
4×	`add-log-exp_binary64_14098` `prod-exp_binary64_14108` `pow1/2_binary64_14139` `cbrt-unprod_binary64_14092` `associate-l_binary64_14000`
2×	`rem-sqrt-square_binary64_14072` `flip--_binary64_14034` `*-commutative_binary64_13990` `unswap-sqr_binary64_14027` `flip3--_binary64_14063`

Counts

4 → 83

Calls

4 calls:

30.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
22.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
7.0ms	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))
4.0ms	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))

series450.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))
120.0ms	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))
95.0ms	(sqrt.f64 (sqrt.f64 (*.f64 z 2)))
90.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2))))

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5183	1525

prune207.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	95	8	103

Error

Counts

103 → 8

Compiler

Compiled 2700 to 1755 computations (35% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`sqrt-prod_binary64_14075`
24×	`associate-r_binary64_13999`
21×	`pow1_binary64_14120`
20×	`add-cbrt-cube_binary64_14095` `add-sqr-sqrt_binary64_14081` `add-exp-log_binary64_14097`
15×	`add-cube-cbrt_binary64_14094` `*-un-lft-identity_binary64_14059`
12×	`associate-*l/_binary64_14002`
10×	`prod-exp_binary64_14108` `cbrt-unprod_binary64_14092` `pow-prod-down_binary64_14130`
5×	`associate-l_binary64_14000`
4×	`add-log-exp_binary64_14098` `sqrt-pow1_binary64_14077`
3×	`flip--_binary64_14034` `*-commutative_binary64_13990` `exp-prod_binary64_14111` `flip3--_binary64_14063`
2×	`unswap-sqr_binary64_14027`
1×	`rem-sqrt-square_binary64_14072` `pow1/2_binary64_14139`

Counts

4 → 95

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
12.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
2.0ms	(sqrt.f64 (exp.f64 t))

series293.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
98.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
48.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
22.0ms	(sqrt.f64 (exp.f64 t))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5080	1820

prune164.0ms (1.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	107	8	115

Error

Counts

115 → 8

Compiler

Compiled 2787 to 1729 computations (38% saved)

regimes1.1s (11.6%)

Accuracy

Total 0.3b remaining (98.4%)

Threshold costs 0.3b (98.4%)

Compiler

Compiled 8768 to 8048 computations (8.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	25
1	30	25

end0.0ms (0%)

sample3.5s (36.7%)

Algorithm

1×

intervals

Results

670.0ms	8000×	body	128	valid
530.0ms	6263×	body	128	invalid
393.0ms	4682×	body	128	nan

Compiler

Compiled 695 to 635 computations (8.6% saved)

Details

analyze1.3s (13.2%)

sample87.0ms (0.9%)

simplify308.0ms (3.2%)

prune9.0ms (0.1%)

localize24.0ms (0.3%)

rewrite35.0ms (0.4%)

series498.0ms (5.2%)

simplify114.0ms (1.2%)

prune139.0ms (1.5%)

localize17.0ms (0.2%)

rewrite44.0ms (0.5%)

series632.0ms (6.6%)

simplify123.0ms (1.3%)

prune169.0ms (1.8%)

localize27.0ms (0.3%)

rewrite71.0ms (0.7%)

series450.0ms (4.7%)

simplify98.0ms (1%)

prune207.0ms (2.2%)

localize17.0ms (0.2%)

rewrite47.0ms (0.5%)

series293.0ms (3.1%)

simplify109.0ms (1.1%)

prune164.0ms (1.7%)

regimes1.1s (11.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (36.7%)

Profiling