Details

analyze1.2s (12.2%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (11.6%)

Results

1.0s	8256×	body	128	valid
91.0ms	818×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.1b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series57.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
23.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

10.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
485×	`cancel-sign-sub-inv_binary64`
369×	`sub-neg_binary64`
190×	`associate-/l*_binary64`
162×	`fma-neg_binary64`

Counts

190 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	4500
1	798	4377
2	3022	4121
3	4988	4121

prune156.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	175	5	180

Error

Counts

180 → 5

Alt Table

Status	Error	Program
✓	0.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
▶	1.1b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	11.8b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
	29.3b	(+.f64 x (/.f64 (fma.f64 -1 z t) (/.f64 a y)))

Compiler

Compiled 4565 to 1470 computations (67.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.5b	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
✓	3.5b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))

series1.6s (16.2%)

Counts

4 → 168

Calls

4 calls:

1.1s	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
304.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
137.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
36.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))

rewrite136.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

304×	`*-un-lft-identity_binary64`
246×	`cbrt-prod_binary64`
245×	`add-sqr-sqrt_binary64`
204×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 285

Calls

4 calls:

31.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
29.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))
16.0ms	(.f64 y (.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
5.0ms	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))

simplify334.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

371×	`associate-r_binary64`
358×	`fma-def_binary64`
203×	`associate-/l*_binary64`
196×	`associate-*r/_binary64`
193×	`associate-/r*_binary64`

Counts

453 → 467

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1977	31132
1	5085	31132

prune977.0ms (9.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	664	1	665
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	665	5	670

Error

Counts

670 → 5

Alt Table

Status	Error	Program
▶	5.9b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
	29.3b	(+.f64 x (/.f64 (fma.f64 -1 z t) (/.f64 a y)))
✓	0.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.1b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 57642 to 26653 computations (53.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))
✓	0.5b	(.f64 y (cbrt.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))))
	3.5b	(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
✓	11.3b	(cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))

series1.6s (16.2%)

Counts

3 → 120

Calls

3 calls:

1.3s

(*.f64 y (cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))))

305.0ms

(cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))

58.0ms

(*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

237×	`*-un-lft-identity_binary64`
168×	`add-sqr-sqrt_binary64`
152×	`times-frac_binary64`
76×	`distribute-lft-out--_binary64`
57×	`add-cube-cbrt_binary64`

Counts

3 → 186

Calls

3 calls:

26.0ms

(*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))

12.0ms

(cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))

3.0ms

(*.f64 y (cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a)))))

simplify238.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

652×	`*-commutative_binary64`
306×	`associate-r_binary64`
306×	`fma-def_binary64`
274×	`associate-+r+_binary64`
234×	`associate-*r/_binary64`

Counts

306 → 374

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1536	22980
1	5252	22980

prune752.0ms (7.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	473	0	473
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	473	5	478

Error

Counts

478 → 5

Alt Table

Status	Error	Program
✓	5.9b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
	29.3b	(+.f64 x (/.f64 (fma.f64 -1 z t) (/.f64 a y)))
✓	0.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.1b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
▶	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 40920 to 20097 computations (50.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	12.3b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))

series43.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

35.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
8.0ms	(*.f64 (-.f64 z t) y)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

7.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
4.0ms	(*.f64 (-.f64 z t) y)

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
304×	`cancel-sign-sub-inv_binary64`
297×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`
241×	`fma-neg_binary64`

Counts

115 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	2434
1	539	2242
2	2070	1972
3	4757	1969
4	4997	1966
5	4976	1966

prune104.0ms (1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	124	5	129

Error

Counts

129 → 5

Alt Table

Status	Error	Program
✓	5.9b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (*.f64 (/.f64 (-.f64 z t) (-.f64 z a)) (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
	29.3b	(+.f64 x (/.f64 (-.f64 t z) (/.f64 a y)))
✓	0.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.1b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))))) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))))
✓	11.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 2824 to 905 computations (68% saved)

regimes991.0ms (9.9%)

Accuracy

Total 1.3b remaining (98.5%)

Threshold costs 0b (0%)

Counts

87 → 1

Compiler

Compiled 16880 to 9488 computations (43.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end97.0ms (1%)

Compiler: Compiled 147 to 76 computations (48.3% saved)

Details

analyze1.2s (12.2%)

sample1.2s (11.6%)

simplify114.0ms (1.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series57.0ms (0.6%)

rewrite27.0ms (0.3%)

simplify104.0ms (1%)

prune156.0ms (1.6%)

localize10.0ms (0.1%)

series1.6s (16.2%)

rewrite136.0ms (1.4%)

simplify334.0ms (3.3%)

prune977.0ms (9.7%)

localize12.0ms (0.1%)

series1.6s (16.2%)

rewrite73.0ms (0.7%)

simplify238.0ms (2.4%)

prune752.0ms (7.5%)

localize8.0ms (0.1%)

series43.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify110.0ms (1.1%)

prune104.0ms (1%)

regimes991.0ms (9.9%)

simplify4.0ms (0%)

end97.0ms (1%)

Profiling