Details

analyze721.0ms (5.9%)

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)

sample52.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
10.0ms	170×	body	128	invalid
7.0ms	126×	body	128	nan

Compiler

Compiled 35 to 37 computations (-5.7% saved)

simplify265.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	4864	25
1	4864	25

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Compiler

Compiled 33 to 31 computations (6.1% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube_binary64_25082`
13×	`add-exp-log_binary64_25084`
10×	`pow1_binary64_25107` `add-sqr-sqrt_binary64_25068`
8×	`add-cube-cbrt_binary64_25081` `*-un-lft-identity_binary64_25046`
7×	`associate-r_binary64_24986`
6×	`associate-*l/_binary64_24989`
5×	`cbrt-unprod_binary64_25079` `prod-exp_binary64_25095`
4×	`associate-l_binary64_24987` `pow-prod-down_binary64_25117`
3×	`times-frac_binary64_25052` `add-log-exp_binary64_25085` `associate-/r*_binary64_24990`
2×	`*-commutative_binary64_24977` `flip3--_binary64_25050` `cbrt-undiv_binary64_25080` `div-exp_binary64_25097` `flip--_binary64_25021`
1×	`div-inv_binary64_25043` `associate-/l*_binary64_24991` `unswap-sqr_binary64_25014` `frac-2neg_binary64_25057` `sqrt-prod_binary64_25062` `clear-num_binary64_25045`

Counts

3 → 62

Calls

6 calls:

13.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
4.0ms	(/.f64 (*.f64 t t) 2)
0.0ms	(/.f64 (*.f64 t t) 2)
0.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))

series799.0ms (6.5%)

Counts

3 → 39

Calls

3 calls:

528.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
244.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
26.0ms	(/.f64 (*.f64 t t) 2)

Compiler

Compiled 1732 to 1556 computations (10.2% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5027	2021

prune145.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Error

0.0b

Counts

102 → 10

Compiler

Compiled 2386 to 1574 computations (34% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`associate-r_binary64_24986`
21×	`pow1_binary64_25107`
20×	`sqrt-prod_binary64_25062` `add-exp-log_binary64_25084` `add-cbrt-cube_binary64_25082`
17×	`add-sqr-sqrt_binary64_25068`
14×	`add-cube-cbrt_binary64_25081` `*-un-lft-identity_binary64_25046`
12×	`associate-*l/_binary64_24989`
10×	`pow-prod-down_binary64_25117` `cbrt-unprod_binary64_25079` `prod-exp_binary64_25095`
6×	`unpow-prod-down_binary64_25125`
5×	`associate-l_binary64_24987`
4×	`add-log-exp_binary64_25085` `sqrt-pow1_binary64_25064`
3×	`*-commutative_binary64_24977` `flip3--_binary64_25050` `exp-prod_binary64_25098` `flip--_binary64_25021`
1×	`pow1/2_binary64_25126` `unswap-sqr_binary64_25014` `sqr-pow_binary64_25018` `rem-sqrt-square_binary64_25059`

Counts

4 → 93

Calls

8 calls:

22.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (exp.f64 (/.f64 (.f64 t t) 2))))
14.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
9.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
2.0ms	(sqrt.f64 (exp.f64 t))
0.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t))

series2.0s (16.3%)

Counts

4 → 63

Calls

4 calls:

982.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 (exp.f64 (/.f64 (.f64 t t) 2))))
734.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
246.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
25.0ms	(sqrt.f64 (exp.f64 t))

Compiler

Compiled 3646 to 2915 computations (20% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5124	4168

prune222.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	156	10	166

Error

0.0b

Counts

166 → 10

Compiler

Compiled 4826 to 2605 computations (46% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.0b	(/.f64 (*.f64 t t) 2)
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))
0.0b	(/.f64 (*.f64 t t) 2)
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))
0.2b	(.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))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64_25082`
22×	`add-exp-log_binary64_25084`
20×	`pow1_binary64_25107`
16×	`add-sqr-sqrt_binary64_25068`
15×	`associate-r_binary64_24986`
12×	`add-cube-cbrt_binary64_25081` `-un-lft-identity_binary64_25046` `associate-l/_binary64_24989`
11×	`cbrt-unprod_binary64_25079` `prod-exp_binary64_25095`
10×	`pow-prod-down_binary64_25117`
7×	`sqrt-prod_binary64_25062`
5×	`associate-l_binary64_24987`
4×	`add-log-exp_binary64_25085`
3×	`times-frac_binary64_25052` `-commutative_binary64_24977` `flip3--_binary64_25050` `associate-/r_binary64_24990` `flip--_binary64_25021`
2×	`unswap-sqr_binary64_25014` `cbrt-undiv_binary64_25080` `div-exp_binary64_25097`
1×	`div-inv_binary64_25043` `associate-/l*_binary64_24991` `frac-2neg_binary64_25057` `clear-num_binary64_25045`

Counts

4 → 91

Calls

8 calls:

16.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))
11.0ms	(.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))
4.0ms	(/.f64 (*.f64 t t) 2)
0.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))

series978.0ms (8%)

Counts

4 → 54

Calls

4 calls:

545.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))
247.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))
159.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
26.0ms	(/.f64 (*.f64 t t) 2)

Compiler

Compiled 2300 to 2061 computations (10.4% saved)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5508	2730

prune174.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Error

Counts

155 → 8

Compiler

Compiled 3252 to 2033 computations (37.5% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.0b	(/.f64 (*.f64 t t) 2)
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))) (exp.f64 (/.f64 (.f64 t t) 2)))
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))) (exp.f64 (/.f64 (.f64 t t) 2)))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.3b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite72.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_25107` `add-cbrt-cube_binary64_25082`
30×	`add-exp-log_binary64_25084`
27×	`associate-r_binary64_24986`
22×	`sqrt-prod_binary64_25062`
20×	`pow-prod-down_binary64_25117` `cbrt-unprod_binary64_25079` `associate-*l/_binary64_24989` `prod-exp_binary64_25095`
18×	`add-sqr-sqrt_binary64_25068`
14×	`add-cube-cbrt_binary64_25081` `*-un-lft-identity_binary64_25046`
6×	`associate-l_binary64_24987`
4×	`*-commutative_binary64_24977` `flip3--_binary64_25050` `add-log-exp_binary64_25085` `flip--_binary64_25021`
2×	`unswap-sqr_binary64_25014`

Counts

4 → 105

Calls

8 calls:

23.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (exp.f64 (/.f64 (.f64 t t) 2)))
17.0ms	(.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))
0.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (exp.f64 (/.f64 (.f64 t t) 2)))

series1.2s (9.9%)

Counts

4 → 66

Calls

4 calls:

552.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (exp.f64 (/.f64 (.f64 t t) 2)))
250.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
246.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
158.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))

Compiler

Compiled 3020 to 2730 computations (9.6% saved)

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4972	3553
1	4972	3553

prune226.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	171	8	179

Error

Counts

179 → 8

Compiler

Compiled 4124 to 2731 computations (33.8% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	476	1034
1	476	1034

regimes770.0ms (6.3%)

Accuracy

Total 0.3b remaining (94%)

Threshold costs 0.3b (94%)

Compiler

Compiled 8726 to 8056 computations (7.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	26
1	30	26

end0.0ms (0%)

sample4.0s (33%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
371.0ms	6113×	body	128	invalid
272.0ms	4551×	body	128	nan

Compiler

Compiled 2023 to 1857 computations (8.2% saved)

Pareto

0.20452950724674598

Details

analyze721.0ms (5.9%)

sample52.0ms (0.4%)

simplify265.0ms (2.2%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite32.0ms (0.3%)

series799.0ms (6.5%)

simplify71.0ms (0.6%)

prune145.0ms (1.2%)

localize22.0ms (0.2%)

rewrite59.0ms (0.5%)

series2.0s (16.3%)

simplify71.0ms (0.6%)

prune222.0ms (1.8%)

localize13.0ms (0.1%)

rewrite47.0ms (0.4%)

series978.0ms (8%)

simplify81.0ms (0.7%)

prune174.0ms (1.4%)

localize19.0ms (0.2%)

rewrite72.0ms (0.6%)

series1.2s (9.9%)

simplify106.0ms (0.9%)

prune226.0ms (1.8%)

simplify23.0ms (0.2%)

regimes770.0ms (6.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.0s (33%)

Profiling