Details

analyze870.0ms (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%	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)

sample39.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	59×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_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)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

10.4b

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

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_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 (0.3%)

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)

simplify85.0ms (0.7%)

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

prune11.0ms (0.1%)

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
	13.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	31.7b	(cbrt.f64 (pow.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)) 3))
✓	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 120 to 73 computations (39.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

6.6b	(/.f64 b1 (/.f64 a2 b2))
7.1b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))

rewrite288.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 266

Calls

2 calls:

13.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
6.0ms	(/.f64 b1 (/.f64 a2 b2))

Compiler

Compiled 5189 to 1256 computations (75.8% saved)

series63.0ms (0.5%)

Error

0.1b

Counts

2 → 21

Calls

2 calls:

39.0ms	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
23.0ms	(/.f64 b1 (/.f64 a2 b2))

Compiler

Compiled 480 to 303 computations (36.9% saved)

simplify347.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-/r/_binary64`
414×	`associate-/l/_binary64`
385×	`div-sub_binary64`
381×	`associate-*l/_binary64`
332×	`associate-*r/_binary64`

Counts

287 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	6532
1	986	6310
2	3704	6307
3	3618	6307
4	4154	6307
5	4438	6307
6	4899	6307
7	5311	6307

prune153.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	6	207
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	202	9	211

Error

Counts

211 → 9

Alt Table

Status	Error	Program
	13.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	10.7b	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))
✓	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.8b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
▶	7.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	11.2b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	24.5b	(*.f64 (sqrt.f64 a2) (/.f64 a1 (/.f64 b1 (/.f64 (sqrt.f64 a2) b2))))
✓	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 3233 to 710 computations (78% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
2.2b	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
2.6b	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))

rewrite3.9s (31.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

5182×	`times-frac_binary64`
2568×	`cbrt-prod_binary64`
2472×	`add-sqr-sqrt_binary64`
2295×	`*-un-lft-identity_binary64`
2295×	`add-cube-cbrt_binary64`

Counts

4 → 2181

Calls

4 calls:

295.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
46.0ms	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
14.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
10.0ms	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))

Compiler

Compiled 100870 to 12220 computations (87.9% saved)

series369.0ms (3%)

Error

Counts

4 → 42

Calls

4 calls:

112.0ms	(/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
105.0ms	(/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (*.f64 (cbrt.f64 a2) (cbrt.f64 a2))))
69.0ms	(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))
60.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))

Compiler

Compiled 3252 to 1983 computations (39% saved)

simplify1.7s (13.7%)

Algorithm

1×	egg-herbie

Rules

914×	`associate-/r/_binary64`
557×	`associate-*l/_binary64`
555×	`associate-*r/_binary64`
143×	`associate-/l*_binary64`
37×	`associate-/r*_binary64`

Counts

2223 → 1900

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1923	99755
1	4966	99755
2	4995	99755

prune959.0ms (7.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1900	0	1900
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	1900	9	1909

Error

Counts

1909 → 9

Alt Table

Status	Error	Program
	13.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
▶	10.7b	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))
✓	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.8b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
✓	7.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	11.2b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	24.5b	(*.f64 (sqrt.f64 a2) (/.f64 a1 (/.f64 b1 (/.f64 (sqrt.f64 a2) b2))))
✓	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 48496 to 3833 computations (92.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 a1)
0.5b	(cbrt.f64 a1)
2.0b	(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
8.2b	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))

rewrite295.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-exp-log_binary64`
31×	`add-cbrt-cube_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
15×	`cbrt-prod_binary64`

Counts

4 → 90

Calls

4 calls:

14.0ms	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))
5.0ms	(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
1.0ms	(cbrt.f64 a1)
1.0ms	(cbrt.f64 a1)

Compiler

Compiled 1831 to 310 computations (83.1% saved)

series133.0ms (1.1%)

Error

Counts

4 → 27

Calls

4 calls:

53.0ms	(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
45.0ms	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))
15.0ms	(cbrt.f64 a1)
14.0ms	(cbrt.f64 a1)

Compiler

Compiled 1042 to 669 computations (35.8% saved)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

816×	`associate-*l/_binary64`
539×	`*-commutative_binary64`
448×	`associate-/r*_binary64`
349×	`log-div_binary64`
299×	`associate-l_binary64`

Counts

117 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1558
1	324	1209
2	1413	1201
3	4066	1201
4	4986	1201
5	5114	1201

prune33.0ms (0.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	77	9	86

Error

Counts

86 → 9

Alt Table

Status	Error	Program
	13.1b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	10.7b	(.f64 (.f64 a2 (.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (.f64 b1 b2)))
	12.7b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.8b	(/.f64 1 (/.f64 b1 (*.f64 a1 (/.f64 a2 b2))))
	7.0b	(.f64 (/.f64 (.f64 (cbrt.f64 a1) (cbrt.f64 a1)) (/.f64 (.f64 (cbrt.f64 b1) (cbrt.f64 b1)) (.f64 (cbrt.f64 a2) (cbrt.f64 a2)))) (/.f64 (cbrt.f64 a1) (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
	11.2b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	24.5b	(*.f64 (sqrt.f64 a2) (/.f64 a1 (/.f64 b1 (/.f64 (sqrt.f64 a2) b2))))
	10.8b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 768 to 278 computations (63.8% saved)

regimes1.8s (14.8%)

Accuracy

Total 2.6b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 23321 to 12988 computations (44.3% saved)

bsearch5.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
1	55	176
2	54	176

end44.0ms (0.4%)

Remove: (sort b1 b2)
Compiler: Compiled 826 to 322 computations (61% saved)

sample1.0s (8.3%)

Algorithm

1×

intervals

Results

204.0ms	8000×	body	128	valid
52.0ms	1882×	body	128	invalid

Compiler

Compiled 267 to 137 computations (48.7% saved)

Details

analyze870.0ms (7%)

sample39.0ms (0.3%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

rewrite30.0ms (0.2%)

series42.0ms (0.3%)

simplify85.0ms (0.7%)

prune11.0ms (0.1%)

localize5.0ms (0%)

rewrite288.0ms (2.3%)

series63.0ms (0.5%)

simplify347.0ms (2.8%)

prune153.0ms (1.2%)

localize22.0ms (0.2%)

rewrite3.9s (31.4%)

series369.0ms (3%)

simplify1.7s (13.7%)

prune959.0ms (7.7%)

localize9.0ms (0.1%)

rewrite295.0ms (2.4%)

series133.0ms (1.1%)

simplify105.0ms (0.9%)

prune33.0ms (0.3%)

regimes1.8s (14.8%)

bsearch5.0ms (0%)

simplify8.0ms (0.1%)

end44.0ms (0.4%)

sample1.0s (8.3%)

Profiling