Details

analyze424.0ms (13.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
9.4%	90.5%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
37.8%	60.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
56.8%	36.2%	7%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify142.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1130×	`div-sub_binary64`
455×	`associate-/l*_binary64`
423×	`sub-neg_binary64`
377×	`associate-*l/_binary64`
366×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	27	10
3	54	10
4	99	10
5	155	10
6	255	10
7	876	10
8	2682	10
9	3301	10
10	3866	10
11	4221	10
12	4255	10
13	4445	10
14	4864	10

prune2.0ms (0.1%)

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

10.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (-.f64 y z))
10.4b	(/.f64 (*.f64 x (-.f64 y z)) y)

rewrite57.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cancel-sign-sub-inv_binary64`

Counts

2 → 53

Calls

2 calls:

10.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
7.0ms	(*.f64 x (-.f64 y z))

Compiler

Compiled 686 to 198 computations (71.1% saved)

series67.0ms (2.2%)

Error

3.5b

Counts

2 → 30

Calls

2 calls:

34.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
26.0ms	(*.f64 x (-.f64 y z))

Compiler

Compiled 526 to 312 computations (40.7% saved)

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

670×	`times-frac_binary64`
645×	`associate-/l*_binary64`
254×	`div-sub_binary64`
250×	`associate-*l/_binary64`
214×	`distribute-rgt-in_binary64`

Counts

83 → 43

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	108	883
1	269	790
2	951	790
3	4220	790
4	5058	790

prune16.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	37.7b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (-.f64 y z)) (sqrt.f64 y))
	35.5b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (-.f64 y z) (sqrt.f64 x))) y)
▶	3.4b	(*.f64 x (/.f64 (-.f64 y z) y))
	39.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3)) y)

Compiler

Compiled 260 to 127 computations (51.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 y z) y)
3.2b	(*.f64 x (/.f64 (-.f64 y z) y))

rewrite75.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

2 → 76

Calls

2 calls:

9.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
6.0ms	(/.f64 (-.f64 y z) y)

Compiler

Compiled 1020 to 242 computations (76.3% saved)

series59.0ms (1.9%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

35.0ms	(*.f64 x (/.f64 (-.f64 y z) y))
19.0ms	(/.f64 (-.f64 y z) y)

Compiler

Compiled 432 to 278 computations (35.6% saved)

simplify102.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

341×	`neg-mul-1_binary64`
303×	`associate-+l+_binary64`
287×	`associate-l_binary64`
262×	`associate-*l/_binary64`
260×	`associate-*r/_binary64`

Counts

103 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1297
1	269	1202
2	859	1200
3	2599	1200
4	4568	1200
5	4989	1200

prune35.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	52	8	60

Error

0.0b

Counts

60 → 8

Alt Table

Status	Error	Program
	30.6b	(.f64 (sqrt.f64 x) (.f64 (-.f64 1 (/.f64 z y)) (sqrt.f64 x)))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
▶	3.4b	(.f64 x (.f64 1 (-.f64 1 (/.f64 z y))))
	8.9b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))
	38.4b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (/.f64 z y)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (/.f64 z y)))))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (/.f64 z y)))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
	37.7b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (-.f64 y z)) (sqrt.f64 y))
	39.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3)) y)

Compiler

Compiled 682 to 309 computations (54.7% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

3.2b	(.f64 x (.f64 1 (-.f64 1 (/.f64 z y))))

rewrite92.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

56×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
52×	`cancel-sign-sub-inv_binary64`
36×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`add-exp-log_binary64`

Counts

1 → 77

Calls

1 calls:

13.0ms

(*.f64 x (*.f64 1 (-.f64 1 (/.f64 z y))))

Compiler

Compiled 1506 to 783 computations (48% saved)

series35.0ms (1.1%)

Error

0.0b

Counts

1 → 15

Calls

1 calls:

32.0ms

(*.f64 x (*.f64 1 (-.f64 1 (/.f64 z y))))

Compiler

Compiled 247 to 156 computations (36.8% saved)

simplify98.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

389×	`unsub-neg_binary64`
357×	`associate-+l+_binary64`
349×	`exp-prod_binary64`
342×	`distribute-rgt-neg-out_binary64`
335×	`distribute-lft-neg-out_binary64`

Counts

92 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	988
1	391	925
2	1108	925
3	2487	924
4	4727	924
5	4961	924

prune24.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	82	9	91

Error

0.0b

Counts

91 → 9

Alt Table

Status	Error	Program
	30.6b	(.f64 (sqrt.f64 x) (.f64 (-.f64 1 (/.f64 z y)) (sqrt.f64 x)))
	17.9b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (/.f64 z y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 z y) (/.f64 z y)) (.f64 1 (/.f64 z y)))))
✓	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
✓	3.4b	(.f64 x (.f64 1 (-.f64 1 (/.f64 z y))))
▶	8.9b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (/.f64 z y)))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
	33.1b	(.f64 (sqrt.f64 (.f64 (-.f64 1 (/.f64 z y)) x)) (sqrt.f64 (*.f64 (-.f64 1 (/.f64 z y)) x)))
	37.7b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (-.f64 y z)) (sqrt.f64 y))
	39.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3)) y)

Compiler

Compiled 470 to 267 computations (43.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 y z))
0.6b	(cbrt.f64 (-.f64 y z))
0.6b	(cbrt.f64 (-.f64 y z))
7.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))

rewrite105.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
30×	`cbrt-div_binary64` `cbrt-prod_binary64`
28×	`associate-r_binary64`
25×	`add-exp-log_binary64`
24×	`times-frac_binary64`

Counts

4 → 114

Calls

4 calls:

23.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))
3.0ms	(cbrt.f64 (-.f64 y z))
3.0ms	(cbrt.f64 (-.f64 y z))
3.0ms	(cbrt.f64 (-.f64 y z))

Compiler

Compiled 3069 to 516 computations (83.2% saved)

series136.0ms (4.4%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

48.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))
26.0ms	(cbrt.f64 (-.f64 y z))
24.0ms	(cbrt.f64 (-.f64 y z))
23.0ms	(cbrt.f64 (-.f64 y z))

Compiler

Compiled 1964 to 1233 computations (37.2% saved)

simplify131.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

538×	`associate-*r/_binary64`
443×	`associate-*l/_binary64`
391×	`associate-/r*_binary64`
355×	`associate-l_binary64`
264×	`associate-r_binary64`

Counts

153 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	205	2877
1	523	2698
2	1890	2698
3	4702	2698
4	5085	2698

prune40.0ms (1.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	99	10	109

Error

Counts

109 → 10

Alt Table

Status	Error	Program
	30.6b	(.f64 (sqrt.f64 x) (.f64 (-.f64 1 (/.f64 z y)) (sqrt.f64 x)))
	17.9b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (/.f64 z y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (/.f64 z y) (/.f64 z y)) (.f64 1 (/.f64 z y)))))
	10.9b	(/.f64 (*.f64 x (-.f64 y z)) y)
	3.4b	(.f64 x (.f64 1 (-.f64 1 (/.f64 z y))))
	8.9b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) y))
	16.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (/.f64 z y)))) (sqrt.f64 (/.f64 (-.f64 y z) y)))
	33.1b	(.f64 (sqrt.f64 (.f64 (-.f64 1 (/.f64 z y)) x)) (sqrt.f64 (*.f64 (-.f64 1 (/.f64 z y)) x)))
	37.7b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (-.f64 y z)) (sqrt.f64 y))
	46.5b	(/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (.f64 x (.f64 (cbrt.f64 (-.f64 (pow.f64 y 3) (pow.f64 z 3))) (cbrt.f64 (-.f64 (.f64 y y) (.f64 z z)))))) (.f64 y (.f64 (cbrt.f64 (+.f64 (.f64 y y) (*.f64 z (+.f64 y z)))) (cbrt.f64 (+.f64 y z)))))
	39.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 x (-.f64 y z)) 3)) y)

Compiler

Compiled 1504 to 444 computations (70.5% saved)

regimes517.0ms (16.9%)

Accuracy

Total 2.7b remaining (99.1%)

Threshold costs 0b (0%)

Compiler

Compiled 4987 to 2799 computations (43.9% saved)

bsearch41.0ms (1.3%)

Steps

Iters	Range		Point
8	9.387097629244738e-207	5.569166256240766e-202	1.519021203658292e-206
9	-2.9458430409886368e-239	-8.9928427914438e-246	-4.213955266002081e-241

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg_binary64` `*-commutative_binary64` `+-commutative_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64`
1×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	57
1	29	57
2	38	57
3	42	57
4	44	57
5	44	57

end1.0ms (0%)

Compiler: Compiled 41 to 21 computations (48.8% saved)

sample743.0ms (24.2%)

Algorithm

1×

intervals

Results

223.0ms	8000×	body	128	valid
24.0ms	766×	body	128	invalid

Compiler

Compiled 252 to 150 computations (40.5% saved)

Details

analyze424.0ms (13.8%)

sample17.0ms (0.6%)

simplify142.0ms (4.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite57.0ms (1.8%)

series67.0ms (2.2%)

simplify73.0ms (2.4%)

prune16.0ms (0.5%)

localize7.0ms (0.2%)

rewrite75.0ms (2.4%)

series59.0ms (1.9%)

simplify102.0ms (3.3%)

prune35.0ms (1.2%)

localize8.0ms (0.3%)

rewrite92.0ms (3%)

series35.0ms (1.1%)

simplify98.0ms (3.2%)

prune24.0ms (0.8%)

localize9.0ms (0.3%)

rewrite105.0ms (3.4%)

series136.0ms (4.4%)

simplify131.0ms (4.3%)

prune40.0ms (1.3%)

regimes517.0ms (16.9%)

bsearch41.0ms (1.3%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample743.0ms (24.2%)

Profiling