Details

analyze934.0ms (12.3%)

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%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample2.9s (38.9%)

Results

1.5s	10811×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
522×	`fma-def_binary64`
417×	`neg-sub0_binary64`
408×	`neg-mul-1_binary64`
378×	`prod-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	51	25
3	102	25
4	219	25
5	464	25
6	1225	25
7	2416	25
8	3703	25
9	4714	25
10	4874	25
11	4224	25
12	4608	25
13	4555	25
14	4942	25

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))

Compiler

Compiled 119 to 89 computations (25.2% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series215.0ms (2.8%)

Counts

3 → 64

Calls

3 calls:

185.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
27.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
2.0ms	(sqrt.f64 (exp.f64 t))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`associate-r_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

11.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
6.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
1.0ms	(sqrt.f64 (exp.f64 t))

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
658×	`fma-def_binary64`
291×	`associate-l_binary64`
267×	`associate-r_binary64`
256×	`distribute-rgt-in_binary64`

Counts

136 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3670
1	495	3220
2	1783	3055
3	4590	3055
4	5133	3055

prune334.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	8	133

Error

0.0b

Counts

133 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (cbrt.f64 (-.f64 (.f64 x 1/2) y))) (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.4b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (.f64 (cbrt.f64 (sqrt.f64 (.f64 z 2))) (cbrt.f64 (sqrt.f64 (.f64 z 2))))) (cbrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
	0.5b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))) (.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	38.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (.f64 2 z))) 3)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	33.8b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3733 to 2207 computations (40.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
✓	0.0b	(exp.f64 (/.f64 (*.f64 t t) 2))
	0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series113.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

109.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
3.0ms	(exp.f64 (/.f64 (*.f64 t t) 2))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`exp-prod_binary64`
7×	`pow1_binary64`
5×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 40

Calls

2 calls:

11.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
2.0ms	(exp.f64 (/.f64 (*.f64 t t) 2))

simplify136.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
570×	`*-commutative_binary64`
366×	`sub-neg_binary64`
269×	`cancel-sign-sub-inv_binary64`
233×	`associate-l_binary64`

Counts

88 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	2783
1	434	2489
2	1500	1952
3	4358	1950
4	4935	1950
5	4998	1950

prune159.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

0.0b

Counts

143 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (cbrt.f64 (-.f64 (.f64 x 1/2) y))) (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.5b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))) (.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))
	38.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (.f64 2 z))) 3)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.4b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (.f64 (cbrt.f64 (sqrt.f64 (.f64 z 2))) (cbrt.f64 (sqrt.f64 (.f64 z 2))))) (cbrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	33.8b	(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (.f64 (sqrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3888 to 2610 computations (32.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))
	0.0b	(exp.f64 (/.f64 (*.f64 t t) 2))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))

series104.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

82.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))
22.0ms	(.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
7×	`associate-l_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 46

Calls

2 calls:

10.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))
6.0ms	(.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2)))

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
357×	`sub-neg_binary64`
280×	`cancel-sign-sub-inv_binary64`
265×	`associate-r_binary64`
229×	`associate-l_binary64`

Counts

94 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	3235
1	453	2900
2	1561	2337
3	4319	2337
4	4916	2337
5	4983	2337

prune131.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	137	8	145

Error

0.0b

Counts

145 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (cbrt.f64 (-.f64 (.f64 x 1/2) y))) (.f64 (cbrt.f64 (-.f64 (.f64 x 1/2) y)) (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	18.4b	(.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (pow.f64 (.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (sqrt.f64 (.f64 2 z))) 3)))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
▶	0.5b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))) (.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))
	38.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (.f64 2 z))) 3)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.4b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (.f64 (cbrt.f64 (sqrt.f64 (.f64 z 2))) (cbrt.f64 (sqrt.f64 (.f64 z 2))))) (cbrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 3888 to 2566 computations (34% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))
✓	0.4b	(.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))
✓	0.4b	(*.f64 (sqrt.f64 2) x)
✓	0.4b	(*.f64 y (sqrt.f64 2))

series32.0ms (0.4%)

Counts

4 → 0

Calls

4 calls:

14.0ms	(.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))
13.0ms	(.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))
3.0ms	(*.f64 y (sqrt.f64 2))
3.0ms	(*.f64 (sqrt.f64 2) x)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`

Counts

4 → 94

Calls

4 calls:

5.0ms	(.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))
5.0ms	(.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))
5.0ms	(*.f64 y (sqrt.f64 2))
4.0ms	(*.f64 (sqrt.f64 2) x)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

528×	`associate-*l/_binary64`
411×	`associate-*r/_binary64`
383×	`*-commutative_binary64`
248×	`associate-l_binary64`
239×	`associate-/l/_binary64`

Counts

94 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	115	1075
1	249	997
2	819	997
3	1090	997
4	1321	997
5	1722	997
6	4138	997
7	4975	997

prune102.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	95	9	104

Error

Counts

104 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.5b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 z))) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.7b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 2) x) (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))) (.f64 (*.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	38.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 1/2 x) y) (sqrt.f64 (.f64 2 z))) 3)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (exp.f64 (/.f64 (*.f64 t t) 2))))
	0.6b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 2) x) (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))) (.f64 (*.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.5b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)) (sqrt.f64 z))) (.f64 (*.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.6b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (sqrt.f64 (sqrt.f64 (.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	1.0b	(.f64 (-.f64 (.f64 1/2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (sqrt.f64 z))) (.f64 (.f64 y (sqrt.f64 2)) (sqrt.f64 z))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

Compiler

Compiled 2982 to 1720 computations (42.3% saved)

regimes1.6s (21.2%)

Accuracy

Total 0.3b remaining (93.5%)

Threshold costs 0.3b (93.5%)

Counts

112 → 1

Compiler

Compiled 39142 to 29794 computations (23.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25
5	30	25

end205.0ms (2.7%)

Compiler: Compiled 300 to 228 computations (24% saved)

Details

analyze934.0ms (12.3%)

sample2.9s (38.9%)

simplify123.0ms (1.6%)

prune4.0ms (0%)

localize12.0ms (0.2%)

series215.0ms (2.8%)

rewrite22.0ms (0.3%)

simplify103.0ms (1.4%)

prune334.0ms (4.4%)

localize10.0ms (0.1%)

series113.0ms (1.5%)

rewrite14.0ms (0.2%)

simplify136.0ms (1.8%)

prune159.0ms (2.1%)

localize13.0ms (0.2%)

series104.0ms (1.4%)

rewrite19.0ms (0.2%)

simplify114.0ms (1.5%)

prune131.0ms (1.7%)

localize16.0ms (0.2%)

series32.0ms (0.4%)

rewrite22.0ms (0.3%)

simplify83.0ms (1.1%)

prune102.0ms (1.3%)

regimes1.6s (21.2%)

simplify3.0ms (0%)

end205.0ms (2.7%)

Profiling