Details

analyze684.0ms (6%)

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)

sample58.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
11.0ms	202×	body	128	invalid
8.0ms	144×	body	128	nan

Compiler

Compiled 35 to 37 computations (-5.7% saved)

simplify262.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (171.0ms)

Iter	Nodes	Cost
0	4864	25
1	4864	25

prune6.0ms (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

0.3b

Counts

2 → 1

Compiler

Compiled 32 to 30 computations (6.3% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_16484`
18×	`add-sqr-sqrt_binary64_16468`
15×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
14×	`associate-r_binary64_16386`
12×	`unpow-prod-down_binary64_16525`
11×	`add-cbrt-cube_binary64_16482`
10×	`sqrt-prod_binary64_16462` `prod-exp_binary64_16495`
9×	`pow1_binary64_16507`
8×	`sqrt-pow1_binary64_16464`
6×	`exp-prod_binary64_16498` `associate-*l/_binary64_16389` `pow-pow_binary64_16518`
4×	`cbrt-unprod_binary64_16479` `add-log-exp_binary64_16485` `associate-l_binary64_16387`
3×	`pow-exp_binary64_16514` `pow-unpow_binary64_16523` `pow-to-exp_binary64_16515`
2×	`*-commutative_binary64_16377` `sqr-pow_binary64_16418` `flip3--_binary64_16450` `pow1/2_binary64_16526` `flip--_binary64_16421`
1×	`rem-sqrt-square_binary64_16459` `unswap-sqr_binary64_16414` `pow-prod-down_binary64_16517` `sqrt-pow2_binary64_16465`

Counts

4 → 92

Calls

8 calls:

16.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
15.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
4.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
3.0ms	(sqrt.f64 (exp.f64 t))
0.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)

series1.0s (8.9%)

Counts

4 → 48

Calls

4 calls:

720.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
237.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
36.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)
23.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 1852 to 1536 computations (17.1% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5014	2586

prune187.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	9	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Error

0.0b

Counts

141 → 10

Compiler

Compiled 3115 to 1780 computations (42.9% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64_16484`
22×	`prod-exp_binary64_16495` `associate-r_binary64_16386`
20×	`add-cbrt-cube_binary64_16482`
19×	`add-sqr-sqrt_binary64_16468`
14×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
13×	`sqrt-prod_binary64_16462`
12×	`pow1_binary64_16507` `associate-*l/_binary64_16389`
10×	`cbrt-unprod_binary64_16479`
6×	`unpow-prod-down_binary64_16525`
5×	`associate-l_binary64_16387`
4×	`sqrt-pow1_binary64_16464` `pow-prod-down_binary64_16517` `add-log-exp_binary64_16485`
3×	`pow-exp_binary64_16514` `exp-prod_binary64_16498` `*-commutative_binary64_16377` `pow-to-exp_binary64_16515` `flip3--_binary64_16450` `flip--_binary64_16421`
2×	`unswap-sqr_binary64_16414`
1×	`rem-sqrt-square_binary64_16459` `sqr-pow_binary64_16418` `pow1/2_binary64_16526`

Counts

4 → 96

Calls

8 calls:

17.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
13.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
2.0ms	(sqrt.f64 (exp.f64 t))
0.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)

series1.1s (10%)

Counts

4 → 57

Calls

4 calls:

730.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
237.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
158.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
23.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 2250 to 1877 computations (16.6% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4970	2975
1	4970	2975

prune181.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	155	8	163

Error

Counts

163 → 8

Compiler

Compiled 3390 to 1842 computations (45.7% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite95.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-exp-log_binary64_16484`
79×	`prod-exp_binary64_16495`
41×	`cbrt-unprod_binary64_16479`
39×	`add-cbrt-cube_binary64_16482`
36×	`pow1_binary64_16507`
26×	`associate-r_binary64_16386`
22×	`pow-prod-down_binary64_16517`
20×	`associate-*l/_binary64_16389`
17×	`add-sqr-sqrt_binary64_16468`
13×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
10×	`sqrt-prod_binary64_16462`
6×	`pow-exp_binary64_16514` `cbrt-prod_binary64_16477` `unpow-prod-down_binary64_16525` `pow-to-exp_binary64_16515` `associate-l_binary64_16387`
4×	`*-commutative_binary64_16377` `add-log-exp_binary64_16485` `flip3--_binary64_16450` `flip--_binary64_16421`
2×	`unswap-sqr_binary64_16414`
1×	`sqr-pow_binary64_16418`

Counts

4 → 128

Calls

8 calls:

28.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
21.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
16.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)

series1.8s (15.7%)

Counts

4 → 66

Calls

4 calls:

753.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
627.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
250.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
169.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))

Compiler

Compiled 3170 to 2744 computations (13.4% saved)

simplify120.0ms (1%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4962	4363
1	4962	4363

prune259.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Compiler

Compiled 4904 to 2955 computations (39.7% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64_16484`
40×	`prod-exp_binary64_16495`
34×	`add-cbrt-cube_binary64_16482` `associate-r_binary64_16386`
25×	`sqrt-prod_binary64_16462`
20×	`pow1_binary64_16507` `cbrt-unprod_binary64_16479` `associate-*l/_binary64_16389` `add-sqr-sqrt_binary64_16468`
16×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
10×	`pow-prod-down_binary64_16517`
6×	`unpow-prod-down_binary64_16525` `associate-l_binary64_16387`
4×	`pow-exp_binary64_16514` `*-commutative_binary64_16377` `add-log-exp_binary64_16485` `pow-to-exp_binary64_16515` `flip3--_binary64_16450` `flip--_binary64_16421`
2×	`unswap-sqr_binary64_16414`
1×	`sqr-pow_binary64_16418`

Counts

4 → 116

Calls

8 calls:

25.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
18.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
14.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.0ms	(pow.f64 (sqrt.f64 (exp.f64 t)) t)

series1.4s (12.4%)

Counts

4 → 66

Calls

4 calls:

748.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
262.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
248.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
162.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))

Compiler

Compiled 2896 to 2482 computations (14.3% saved)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5006	3871

prune225.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	183	7	190

Error

Counts

190 → 7

Compiler

Compiled 4236 to 2447 computations (42.2% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	547	1163
1	547	1163

regimes632.0ms (5.5%)

Compiler: Compiled 6891 to 6461 computations (6.2% saved)

bsearch0.0ms (0%)

regimes189.0ms (1.6%)

Compiler: Compiled 1420 to 1484 computations (-4.5% saved)

bsearch0.0ms (0%)

regimes92.0ms (0.8%)

Compiler: Compiled 360 to 472 computations (-31.1% saved)

bsearch0.0ms (0%)

regimes64.0ms (0.6%)

Compiler: Compiled 102 to 214 computations (-109.8% saved)

bsearch0.0ms (0%)

regimes35.0ms (0.3%)

Accuracy

Total 0.3b remaining (94.8%)

Threshold costs 0.3b (94.8%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch5.0ms (0%)

Compiler: Compiled 63 to 69 computations (-9.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	95
1	44	95

end0.0ms (0%)

sample2.5s (21.4%)

Algorithm

1×

intervals

Results

435.0ms	8000×	body	128	valid
335.0ms	6048×	body	128	invalid
239.0ms	4410×	body	128	nan

Compiler

Compiled 840 to 790 computations (6% saved)

Pareto

0.7300072916815905

Details

analyze684.0ms (6%)

sample58.0ms (0.5%)

simplify262.0ms (2.3%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

rewrite47.0ms (0.4%)

series1.0s (8.9%)

simplify96.0ms (0.8%)

prune187.0ms (1.6%)

localize14.0ms (0.1%)

rewrite53.0ms (0.5%)

series1.1s (10%)

simplify83.0ms (0.7%)

prune181.0ms (1.6%)

localize18.0ms (0.2%)

rewrite95.0ms (0.8%)

series1.8s (15.7%)

simplify120.0ms (1%)

prune259.0ms (2.3%)

localize19.0ms (0.2%)

rewrite79.0ms (0.7%)

series1.4s (12.4%)

simplify91.0ms (0.8%)

prune225.0ms (2%)

simplify24.0ms (0.2%)

regimes632.0ms (5.5%)

bsearch0.0ms (0%)

regimes189.0ms (1.6%)

bsearch0.0ms (0%)

regimes92.0ms (0.8%)

bsearch0.0ms (0%)

regimes64.0ms (0.6%)

bsearch0.0ms (0%)

regimes35.0ms (0.3%)

bsearch5.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (21.4%)

Profiling