Details

analyze385.0ms (4.7%)

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%	68.6%	31.4%	5
0%	65.5%	34.5%	6
0%	59.2%	40.8%	7
0%	51.4%	48.6%	8
0%	41.3%	58.7%	9
0%	28.4%	71.6%	10
2.3%	22.3%	75.4%	11
2.3%	21%	76.7%	12
2.7%	18%	79.3%	13
2.7%	16.4%	80.8%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
11.0ms	148×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 33 to 36 computations (-9.1% saved)

simplify271.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	1362	25
1	1362	25

prune3.0ms (0%)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 32 to 30 computations (6.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
0.1b	(*.f64 (-.f64 a 1/2) (log.f64 t))
0.1b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_4551`
20×	`add-sqr-sqrt_binary64_4573`
19×	`log-prod_binary64_4637`
15×	`pow1_binary64_4612`
14×	`add-log-exp_binary64_4590` `add-cube-cbrt_binary64_4586`
9×	`log-pow_binary64_4640` `associate-+l+_binary64_4484` `distribute-lft-out_binary64_4502` `associate-+r+_binary64_4483`
6×	`sum-log_binary64_4642` `flip--_binary64_4526` `distribute-rgt-in_binary64_4501` `associate-*l/_binary64_4494` `flip3--_binary64_4555` `add-exp-log_binary64_4589` `add-cbrt-cube_binary64_4587` `distribute-lft-out--_binary64_4503` `distribute-lft-in_binary64_4500` `cancel-sign-sub-inv_binary64_4517`
5×	`associate-+l-_binary64_4486` `associate-l_binary64_4492`
4×	`diff-log_binary64_4643` `log-div_binary64_4638` `frac-add_binary64_4559` `associate-r_binary64_4491` `flip3-+_binary64_4554` `flip-+_binary64_4525`
2×	`difference-of-squares_binary64_4520` `associate--l+_binary64_4488` `sub-neg_binary64_4544` `+-commutative_binary64_4481` `associate--l-_binary64_4489`
1×	`*-commutative_binary64_4482` `prod-exp_binary64_4600` `unswap-sqr_binary64_4519` `cbrt-unprod_binary64_4584` `pow-prod-down_binary64_4622`

Counts

4 → 106

Calls

4 calls:

17.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
13.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))
10.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
9.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series797.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

373.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
251.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
97.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
76.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4978	2455
1	4978	2455

prune615.0ms (7.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	9	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 0.0b

Counts

119 → 9

Compiler

Compiled 12899 to 7327 computations (43.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z))))
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`log-prod_binary64_4637`
18×	`*-un-lft-identity_binary64_4551` `associate-+r+_binary64_4483`
15×	`cbrt-prod_binary64_4582`
13×	`add-sqr-sqrt_binary64_4573` `add-cube-cbrt_binary64_4586`
7×	`add-log-exp_binary64_4590`
6×	`associate-+l-_binary64_4486` `distribute-rgt-in_binary64_4501` `distribute-lft-in_binary64_4500`
5×	`pow1_binary64_4612` `associate-+l+_binary64_4484`
4×	`sum-log_binary64_4642` `log-div_binary64_4638` `add-exp-log_binary64_4589` `flip3-+_binary64_4554` `flip-+_binary64_4525` `add-cbrt-cube_binary64_4587`
3×	`distribute-lft-out_binary64_4502`
2×	`+-commutative_binary64_4481` `pow1/3_binary64_4633`
1×	`log-pow_binary64_4640`

Counts

4 → 74

Calls

4 calls:

10.0ms	(+.f64 (+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
9.0ms	(+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z))))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

series689.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(+.f64 (+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
180.0ms	(cbrt.f64 z)
173.0ms	(+.f64 (log.f64 (+.f64 x y)) (*.f64 2 (log.f64 (cbrt.f64 z))))
148.0ms	(cbrt.f64 z)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4875	1188
1	4875	1188

prune111.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 0.0b

Counts

95 → 9

Compiler

Compiled 2625 to 1190 computations (54.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.5b	(cbrt.f64 t)
0.5b	(cbrt.f64 t)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`frac-add_binary64_4559`
16×	`*-un-lft-identity_binary64_4551` `add-log-exp_binary64_4590`
14×	`flip--_binary64_4526` `flip3--_binary64_4555`
12×	`associate-*r/_binary64_4493`
11×	`associate-+r+_binary64_4483`
10×	`add-sqr-sqrt_binary64_4573` `add-cube-cbrt_binary64_4586`
9×	`sum-log_binary64_4642`
8×	`associate-*l/_binary64_4494` `pow1_binary64_4612`
7×	`log-prod_binary64_4637`
6×	`cancel-sign-sub-inv_binary64_4517` `cbrt-prod_binary64_4582`
5×	`associate-+l+_binary64_4484` `distribute-lft-out_binary64_4502` `flip3-+_binary64_4554` `flip-+_binary64_4525`
4×	`associate-+l-_binary64_4486` `distribute-rgt-in_binary64_4501` `log-pow_binary64_4640` `add-exp-log_binary64_4589` `add-cbrt-cube_binary64_4587` `distribute-lft-in_binary64_4500`
2×	`diff-log_binary64_4643` `log-div_binary64_4638` `sub-neg_binary64_4544` `+-commutative_binary64_4481` `pow1/3_binary64_4633`

Counts

4 → 82

Calls

4 calls:

21.0ms	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
11.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series1.0s (12.7%)

Counts

4 → 12

Calls

4 calls:

622.0ms	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) (-.f64 a 1/2)))
165.0ms	(cbrt.f64 t)
157.0ms	(cbrt.f64 t)
97.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5066	3949

prune335.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	94	9	103

Merged error: 0.0b

Counts

103 → 9

Compiler

Compiled 7525 to 4091 computations (45.6% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (pow.f64 t 1/3)) (-.f64 a 1/2)))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.5b	(cbrt.f64 t)
5.0b	(pow.f64 t 1/3)

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`frac-add_binary64_4559`
17×	`*-un-lft-identity_binary64_4551`
16×	`add-log-exp_binary64_4590`
14×	`flip--_binary64_4526` `flip3--_binary64_4555`
12×	`associate-*r/_binary64_4493`
11×	`add-sqr-sqrt_binary64_4573` `associate-+r+_binary64_4483` `add-cube-cbrt_binary64_4586`
9×	`sum-log_binary64_4642` `pow1_binary64_4612`
8×	`associate-*l/_binary64_4494`
7×	`log-prod_binary64_4637`
6×	`cancel-sign-sub-inv_binary64_4517`
5×	`associate-+l+_binary64_4484` `distribute-lft-out_binary64_4502` `add-exp-log_binary64_4589` `flip3-+_binary64_4554` `flip-+_binary64_4525`
4×	`associate-+l-_binary64_4486` `distribute-rgt-in_binary64_4501` `log-pow_binary64_4640` `add-cbrt-cube_binary64_4587` `distribute-lft-in_binary64_4500`
3×	`pow-unpow_binary64_4628` `unpow-prod-down_binary64_4630` `cbrt-prod_binary64_4582`
2×	`diff-log_binary64_4643` `log-div_binary64_4638` `sub-neg_binary64_4544` `+-commutative_binary64_4481`
1×	`sqr-pow_binary64_4523` `unpow1/3_binary64_4618` `pow-to-exp_binary64_4620` `pow-pow_binary64_4623` `pow-exp_binary64_4619` `pow1/3_binary64_4633`

Counts

4 → 89

Calls

4 calls:

22.0ms	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (pow.f64 t 1/3)) (-.f64 a 1/2)))
8.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
2.0ms	(pow.f64 t 1/3)
1.0ms	(cbrt.f64 t)

series1.2s (14.2%)

Counts

4 → 12

Calls

4 calls:

788.0ms	(+.f64 (+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (pow.f64 t 1/3)) (-.f64 a 1/2)))
155.0ms	(cbrt.f64 t)
134.0ms	(pow.f64 t 1/3)
91.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4956	4066
1	4956	4066

prune198.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Merged error: 0.0b

Counts

110 → 9

Compiler

Compiled 4975 to 2387 computations (52% saved)

regimes294.0ms (3.6%)

Compiler: Compiled 3042 to 2405 computations (20.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms (0%)

sample1.7s (20.4%)

Algorithm

1×

intervals

Results

656.0ms	8000×	body	128	valid
311.0ms	4413×	body	128	nan
2.0ms	29×	body	128	invalid

Compiler

Compiled 312 to 250 computations (19.9% saved)

Details

analyze385.0ms (4.7%)

sample48.0ms (0.6%)

simplify271.0ms (3.3%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite59.0ms (0.7%)

series797.0ms (9.7%)

simplify73.0ms (0.9%)

prune615.0ms (7.5%)

localize20.0ms (0.2%)

rewrite29.0ms (0.4%)

series689.0ms (8.4%)

simplify78.0ms (0.9%)

prune111.0ms (1.4%)

localize20.0ms (0.2%)

rewrite47.0ms (0.6%)

series1.0s (12.7%)

simplify97.0ms (1.2%)

prune335.0ms (4.1%)

localize28.0ms (0.3%)

rewrite48.0ms (0.6%)

series1.2s (14.2%)

simplify80.0ms (1%)

prune198.0ms (2.4%)

regimes294.0ms (3.6%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (20.4%)

Profiling