Details

analyze369.0ms (5.5%)

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)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
10.0ms	147×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 33 to 36 computations (-9.1% saved)

simplify254.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

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

rewrite57.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_14231`
19×	`log-prod_binary64_14314`
18×	`add-sqr-sqrt_binary64_14252`
15×	`pow1_binary64_14289`
14×	`add-log-exp_binary64_14267`
12×	`add-cube-cbrt_binary64_14263`
9×	`distribute-lft-out_binary64_14184` `associate-+r+_binary64_14165` `log-pow_binary64_14317`
6×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266` `flip3--_binary64_14235` `sum-log_binary64_14319` `distribute-lft-in_binary64_14182` `associate-+l+_binary64_14166` `flip--_binary64_14206` `distribute-rgt-in_binary64_14183` `associate-*l/_binary64_14176` `distribute-lft-out--_binary64_14185`
5×	`associate-+l-_binary64_14168` `associate-l_binary64_14174`
4×	`log-div_binary64_14315` `flip3-+_binary64_14234` `flip-+_binary64_14205` `associate-r_binary64_14173` `diff-log_binary64_14320` `frac-add_binary64_14239`
2×	`+-commutative_binary64_14163` `associate--l-_binary64_14171` `difference-of-squares_binary64_14200` `sub-neg_binary64_14224` `associate--l+_binary64_14170`
1×	`prod-exp_binary64_14277` `pow-prod-down_binary64_14299` `unswap-sqr_binary64_14199` `*-commutative_binary64_14164` `cbrt-unprod_binary64_14261`

Counts

4 → 100

Calls

4 calls:

20.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
10.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
9.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))
9.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series766.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
238.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
92.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
75.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4962	2414
1	4962	2414

prune154.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

Compiler

Compiled 2977 to 1183 computations (60.3% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (log.f64 z) (log.f64 z))
0.6b	(-.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.7b	(pow.f64 (log.f64 (+.f64 x y)) 3)
0.7b	(pow.f64 (log.f64 z) 3)

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64_14289`
26×	`*-un-lft-identity_binary64_14231`
22×	`add-sqr-sqrt_binary64_14252`
18×	`add-cube-cbrt_binary64_14263`
14×	`log-pow_binary64_14317`
13×	`log-prod_binary64_14314`
8×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266` `cube-prod_binary64_14256` `unpow-prod-down_binary64_14307`
6×	`swap-sqr_binary64_14198` `pow-unpow_binary64_14305`
4×	`add-log-exp_binary64_14267` `associate-l_binary64_14174` `associate-r_binary64_14173` `distribute-lft-out--_binary64_14185` `associate--l+_binary64_14170`
3×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183` `associate--r+_binary64_14169`
2×	`pow-pow_binary64_14300` `log-div_binary64_14315` `unpow3_binary64_14294` `associate--l-_binary64_14171` `cube-mult_binary64_14258` `sqr-pow_binary64_14203` `rem-cube-cbrt_binary64_14253` `pow-exp_binary64_14296` `pow-to-exp_binary64_14297`
1×	`distribute-lft-out_binary64_14184` `flip3--_binary64_14235` `flip3-+_binary64_14234` `pow-plus_binary64_14291` `prod-exp_binary64_14277` `pow-prod-down_binary64_14299` `pow2_binary64_14309` `flip-+_binary64_14205` `difference-of-squares_binary64_14200` `unswap-sqr_binary64_14199` `diff-log_binary64_14320` `flip--_binary64_14206` `*-commutative_binary64_14164` `sub-neg_binary64_14224` `pow-sqr_binary64_14204` `pow-prod-up_binary64_14298` `cbrt-unprod_binary64_14261`

Counts

4 → 111

Calls

4 calls:

11.0ms	(-.f64 (log.f64 (+.f64 x y)) (log.f64 z))
6.0ms	(*.f64 (log.f64 z) (log.f64 z))
3.0ms	(pow.f64 (log.f64 (+.f64 x y)) 3)
3.0ms	(pow.f64 (log.f64 z) 3)

series793.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

438.0ms	(pow.f64 (log.f64 (+.f64 x y)) 3)
144.0ms	(pow.f64 (log.f64 z) 3)
110.0ms	(*.f64 (log.f64 z) (log.f64 z))
101.0ms	(-.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4927	1195
1	4927	1195

prune201.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	123	10	133

Merged error: 0.0b

Counts

133 → 10

Compiler

Compiled 5468 to 1952 computations (64.3% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`log-prod_binary64_14314`
30×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183`
28×	`associate-+l+_binary64_14166`
26×	`*-un-lft-identity_binary64_14231`
24×	`cbrt-prod_binary64_14259`
20×	`add-sqr-sqrt_binary64_14252` `add-cube-cbrt_binary64_14263`
15×	`associate-+r+_binary64_14165`
8×	`pow1_binary64_14289` `associate-*l/_binary64_14176`
6×	`distribute-lft-out_binary64_14184` `add-log-exp_binary64_14267`
4×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266` `flip3--_binary64_14235` `flip--_binary64_14206` `frac-add_binary64_14239` `log-pow_binary64_14317`
3×	`flip3-+_binary64_14234` `flip-+_binary64_14205`
2×	`+-commutative_binary64_14163` `log-div_binary64_14315` `associate-+l-_binary64_14168` `sum-log_binary64_14319` `pow1/3_binary64_14310`

Counts

4 → 98

Calls

4 calls:

18.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
8.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series634.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
151.0ms	(cbrt.f64 t)
147.0ms	(cbrt.f64 t)
90.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5673	1664

prune168.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Merged error: 0.0b

Counts

120 → 9

Compiler

Compiled 3707 to 1658 computations (55.3% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (pow.f64 t 1/3))))
0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.6b	(cbrt.f64 t)
4.9b	(pow.f64 t 1/3)

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`log-prod_binary64_14314`
31×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183`
28×	`associate-+l+_binary64_14166`
27×	`*-un-lft-identity_binary64_14231`
21×	`add-sqr-sqrt_binary64_14252` `add-cube-cbrt_binary64_14263`
17×	`associate-+r+_binary64_14165`
15×	`cbrt-prod_binary64_14259`
9×	`pow1_binary64_14289` `unpow-prod-down_binary64_14307`
8×	`associate-*l/_binary64_14176`
6×	`distribute-lft-out_binary64_14184` `add-log-exp_binary64_14267`
5×	`add-exp-log_binary64_14266`
4×	`add-cbrt-cube_binary64_14264` `flip3--_binary64_14235` `flip--_binary64_14206` `frac-add_binary64_14239` `log-pow_binary64_14317`
3×	`flip3-+_binary64_14234` `flip-+_binary64_14205` `sqr-pow_binary64_14203` `pow-unpow_binary64_14305`
2×	`+-commutative_binary64_14163` `log-div_binary64_14315` `associate-+l-_binary64_14168` `sum-log_binary64_14319`
1×	`pow-pow_binary64_14300` `unpow1/3_binary64_14295` `pow-exp_binary64_14296` `pow1/3_binary64_14310` `pow-to-exp_binary64_14297`

Counts

4 → 107

Calls

4 calls:

18.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (pow.f64 t 1/3))))
8.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
2.0ms	(pow.f64 t 1/3)
1.0ms	(cbrt.f64 t)

series710.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (pow.f64 t 1/3))))
158.0ms	(cbrt.f64 t)
142.0ms	(pow.f64 t 1/3)
90.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4882	1745
1	4882	1745

prune166.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 0.0b

Counts

128 → 9

Compiler

Compiled 3778 to 1818 computations (51.9% saved)

regimes268.0ms (4%)

Compiler: Compiled 3238 to 2300 computations (29% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	44
1	49	44

end0.0ms (0%)

sample1.6s (24.4%)

Algorithm

1×

intervals

Results

640.0ms	8000×	body	128	valid
292.0ms	4252×	body	128	nan
2.0ms	26×	body	128	invalid

Compiler

Compiled 380 to 279 computations (26.6% saved)

Details

analyze369.0ms (5.5%)

sample45.0ms (0.7%)

simplify254.0ms (3.8%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite57.0ms (0.8%)

series766.0ms (11.4%)

simplify113.0ms (1.7%)

prune154.0ms (2.3%)

localize26.0ms (0.4%)

rewrite37.0ms (0.6%)

series793.0ms (11.8%)

simplify74.0ms (1.1%)

prune201.0ms (3%)

localize24.0ms (0.4%)

rewrite41.0ms (0.6%)

series634.0ms (9.4%)

simplify52.0ms (0.8%)

prune168.0ms (2.5%)

localize28.0ms (0.4%)

rewrite44.0ms (0.7%)

series710.0ms (10.5%)

simplify53.0ms (0.8%)

prune166.0ms (2.5%)

regimes268.0ms (4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (24.4%)

Profiling