Details

analyze958.0ms (18.6%)

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%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample35.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
2.0ms	67×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-/r/_binary64` `associate-*r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`
4×	`times-frac_binary64` `associate-/l/_binary64` `associate-*l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	63	10
4	69	10
5	68	10
6	68	10

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

10.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

10.6b

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`prod-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `cbrt-unprod_binary64`
1×	`pow1_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-2neg_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l_binary64` `associate-/r*_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

Compiler

Compiled 295 to 77 computations (73.9% saved)

series42.0ms (0.8%)

Error

10.8b

Counts

1 → 12

Calls

1 calls:

41.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

Compiler

Compiled 275 to 175 computations (36.4% saved)

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
393×	`associate-l_binary64`
381×	`associate-*l/_binary64`
297×	`associate-*r/_binary64`
271×	`associate-r_binary64`

Counts

33 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	475
1	155	370
2	779	370
3	3457	370
4	3762	370
5	4079	370
6	4763	370
7	5076	370

prune9.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	8	3	11
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Error

0.1b

Counts

12 → 4

Alt Table

Status	Error	Program
▶	7.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	32.3b	(cbrt.f64 (pow.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)) 3))
✓	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	11.9b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

Compiler

Compiled 120 to 73 computations (39.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.0b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
5.4b	(*.f64 a2 (/.f64 a1 b1))

rewrite66.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`times-frac_binary64` `associate-r_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
5×	`div-exp_binary64` `cbrt-undiv_binary64`

Counts

2 → 56

Calls

2 calls:

7.0ms	(*.f64 a2 (/.f64 a1 b1))
6.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

Compiler

Compiled 740 to 212 computations (71.4% saved)

series71.0ms (1.4%)

Error

0.1b

Counts

2 → 21

Calls

2 calls:

42.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
27.0ms	(*.f64 a2 (/.f64 a1 b1))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify112.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

919×	`times-frac_binary64`
527×	`associate-/l/_binary64`
421×	`associate-l_binary64`
340×	`associate-r_binary64`
297×	`associate-/r/_binary64`

Counts

77 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	108	929
1	263	800
2	1046	800
3	4062	800
4	4579	800
5	4958	800
6	4967	800

prune36.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	31	8	39
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	33	10	43

Error

0.0b

Counts

43 → 10

Alt Table

Status	Error	Program
✓	7.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	9.6b	(/.f64 (.f64 (.f64 a1 a2) (/.f64 1 b1)) b2)
▶	8.4b	(/.f64 (.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1))) b2)
	21.8b	(/.f64 (.f64 (sqrt.f64 a2) (.f64 (/.f64 a1 b1) (sqrt.f64 a2))) b2)
	28.9b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 3)) b2)
	9.5b	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	21.8b	(/.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 (sqrt.f64 b2))) (sqrt.f64 b2))
	8.5b	(/.f64 (.f64 (/.f64 a1 b1) (/.f64 a2 (.f64 (cbrt.f64 b2) (cbrt.f64 b2)))) (cbrt.f64 b2))
	11.9b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	11.3b	(.f64 a2 (/.f64 a1 (.f64 b1 b2)))

Compiler

Compiled 580 to 268 computations (53.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 b1)
0.6b	(cbrt.f64 b1)
4.0b	(/.f64 (.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1))) b2)
4.1b	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1)))

rewrite134.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

54×	`add-exp-log_binary64`
40×	`add-cbrt-cube_binary64`
39×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1)))
12.0ms	(/.f64 (.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1))) b2)
1.0ms	(cbrt.f64 b1)
1.0ms	(cbrt.f64 b1)

Compiler

Compiled 2556 to 464 computations (81.8% saved)

series127.0ms (2.5%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

54.0ms	(/.f64 (.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1))) b2)
33.0ms	(.f64 (/.f64 a2 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (cbrt.f64 b1)))
17.0ms	(cbrt.f64 b1)
16.0ms	(cbrt.f64 b1)

Compiler

Compiled 854 to 549 computations (35.7% saved)

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

237×	`sub-neg_binary64`
236×	`log-prod_binary64`
226×	`associate-/l*_binary64`
217×	`cube-prod_binary64`
215×	`associate-*r/_binary64`

Counts

142 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	3083
1	532	1719
2	2392	1708
3	3463	1706
4	4971	1706

prune58.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	98	10	108

Error

0.0b

Counts

108 → 10

Alt Table

Status	Error	Program
✓	7.7b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	9.6b	(/.f64 (.f64 (.f64 a1 a2) (/.f64 1 b1)) b2)
	21.8b	(/.f64 (.f64 (sqrt.f64 a2) (.f64 (/.f64 a1 b1) (sqrt.f64 a2))) b2)
	28.9b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 3)) b2)
▶	9.5b	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	10.1b	(/.f64 (/.f64 (/.f64 (.f64 a1 a2) b1) (.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (cbrt.f64 b2))
	21.8b	(/.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 (sqrt.f64 b2))) (sqrt.f64 b2))
	11.9b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	23.5b	(/.f64 (/.f64 (/.f64 (*.f64 a1 a2) b1) (sqrt.f64 b2)) (sqrt.f64 b2))
	11.3b	(.f64 a2 (/.f64 a1 (.f64 b1 b2)))

Compiler

Compiled 1381 to 578 computations (58.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

4.0b	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
6.7b	(/.f64 (*.f64 a1 a2) b1)

rewrite102.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64`
19×	`add-exp-log_binary64`
12×	`associate-/l*_binary64`
9×	`div-exp_binary64` `add-cbrt-cube_binary64`

Counts

2 → 84

Calls

2 calls:

6.0ms	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
4.0ms	(/.f64 (*.f64 a1 a2) b1)

Compiler

Compiled 1499 to 621 computations (58.6% saved)

series74.0ms (1.4%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

44.0ms	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
28.0ms	(/.f64 (*.f64 a1 a2) b1)

Compiler

Compiled 518 to 341 computations (34.2% saved)

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-*l/_binary64`
592×	`associate-l_binary64`
451×	`associate-*r/_binary64`
449×	`associate-/r*_binary64`
377×	`associate-/r/_binary64`

Counts

105 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1614
1	279	1489
2	1187	1486
3	4507	1486
4	5049	1486

prune47.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	3	5	8
Picked	0	1	1
Done	1	0	1
Total	69	11	80

Error

Counts

80 → 11

Alt Table

Status	Error	Program
	28.9b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 3)) b2)
	9.5b	(/.f64 (pow.f64 (/.f64 (*.f64 a1 a2) b1) 1) b2)
	34.3b	(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) b1)) (cbrt.f64 b2)))
	10.1b	(/.f64 (/.f64 (/.f64 (.f64 a1 a2) b1) (.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (cbrt.f64 b2))
	21.8b	(/.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 (sqrt.f64 b2))) (sqrt.f64 b2))
	12.1b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	7.5b	(.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (*.f64 (cbrt.f64 b2) (cbrt.f64 b2))) (/.f64 (/.f64 a2 (cbrt.f64 b1)) (cbrt.f64 b2)))
	10.1b	(/.f64 (pow.f64 (*.f64 a1 (/.f64 a2 b1)) 1) b2)
	11.9b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	50.2b	(*.f64 (/.f64 a1 (sqrt.f64 b1)) (/.f64 (/.f64 a2 (sqrt.f64 b1)) b2))
	11.3b	(.f64 a2 (/.f64 a1 (.f64 b1 b2)))

Compiler

Compiled 871 to 296 computations (66% saved)

regimes1.5s (30%)

Accuracy

Total 2.5b remaining (98.9%)

Threshold costs 0b (0%)

Compiler

Compiled 11387 to 6535 computations (42.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`unpow1_binary64`
2×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	137
1	53	137
2	52	137

end39.0ms (0.8%)

Compiler: Compiled 475 to 190 computations (60% saved)

sample1.3s (25.6%)

Algorithm

1×

intervals

Results

248.0ms	8000×	body	128	valid
56.0ms	1933×	body	128	invalid

Compiler

Compiled 283 to 152 computations (46.3% saved)

Details

analyze958.0ms (18.6%)

sample35.0ms (0.7%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite32.0ms (0.6%)

series42.0ms (0.8%)

simplify94.0ms (1.8%)

prune9.0ms (0.2%)

localize6.0ms (0.1%)

rewrite66.0ms (1.3%)

series71.0ms (1.4%)

simplify112.0ms (2.2%)

prune36.0ms (0.7%)

localize12.0ms (0.2%)

rewrite134.0ms (2.6%)

series127.0ms (2.5%)

simplify108.0ms (2.1%)

prune58.0ms (1.1%)

localize10.0ms (0.2%)

rewrite102.0ms (2%)

series74.0ms (1.4%)

simplify91.0ms (1.8%)

prune47.0ms (0.9%)

regimes1.5s (30%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end39.0ms (0.8%)

sample1.3s (25.6%)

Profiling