Details

analyze854.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

sample100.0ms

Algorithm

intervals

Results

28.0ms	335×	body	80	nan
18.0ms	236×	body	80	valid
13.0ms	173×	body	80	invalid
2.0ms	2×	body	1280	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	3×	body	640	valid
1.0ms	6×	body	160	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4997	17
1	4997	17

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 2.0b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 y (-.f64 (log.f64 z) t))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))
0.3b	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))))
5.8b	(log.f64 (-.f64 1.0 z))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod_binary64` `add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
22×	`associate--l+_binary64`
15×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`associate-+r+_binary64`
10×	`pow1_binary64` `associate-r_binary64` `associate-*r/_binary64`
8×	`associate-+l+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-l_binary64` `flip--_binary64`
5×	`distribute-lft-out--_binary64`
4×	`frac-add_binary64` `difference-of-squares_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `log-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `rem-log-exp_binary64` `exp-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 101

Calls

4 calls:

8.0ms	(*.f64 y (-.f64 (log.f64 z) t))
13.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))
13.0ms	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))))
4.0ms	(log.f64 (-.f64 1.0 z))

series133.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 y (-.f64 (log.f64 z) t))
44.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))
71.0ms	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 1.0 z)) b)))))
3.0ms	(log.f64 (-.f64 1.0 z))

simplify77.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4971	1656
1	4971	1656

prune139.0ms

Filtered

90 candidates to 113 candidates (-25.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	4	115

Merged error: 0.3b

Counts

115 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))
0.1b	(*.f64 y (-.f64 (log.f64 z) t))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
0.3b	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (*.f64 1.0 1.0))))) b)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

26×	`associate--l+_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `log-prod_binary64`
15×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
10×	`associate-r_binary64` `associate-*r/_binary64` `associate-+r+_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
8×	`sub-neg_binary64` `associate-+l+_binary64` `add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`frac-add_binary64`
3×	`exp-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `log-pow_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 96

Calls

4 calls:

15.0ms	(exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))
8.0ms	(*.f64 y (-.f64 (log.f64 z) t))
20.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
18.0ms	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (*.f64 1.0 1.0))))) b)))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))
15.0ms	(*.f64 y (-.f64 (log.f64 z) t))
60.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
104.0ms	(.f64 x (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (*.f64 1.0 1.0))))) b)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4975	2646
1	4975	2646

prune169.0ms

Filtered

85 candidates to 108 candidates (-27.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
0.2b	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate--l+_binary64`
24×	`log-prod_binary64`
20×	`associate-+r+_binary64`
18×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `add-sqr-sqrt_binary64`
16×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `associate-+l+_binary64`
12×	`sub-neg_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `frac-add_binary64` `sqrt-pow1_binary64` `flip--_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `exp-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `rem-sqrt-square_binary64` `exp-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 100

Calls

4 calls:

14.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
14.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
18.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
19.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
100.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
61.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
63.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 z) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5045	3766

prune302.0ms

Filtered

101 candidates to 112 candidates (-10.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	112	5	117

Merged error: 0.0b

Counts

117 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
0.3b	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
0.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))) 3))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate--l+_binary64`
24×	`log-prod_binary64`
20×	`add-sqr-sqrt_binary64` `associate-+r+_binary64` `cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
16×	`associate-*r/_binary64` `associate-+l+_binary64`
12×	`sub-neg_binary64` `sqrt-prod_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `frac-add_binary64` `flip--_binary64`
7×	`unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64`
3×	`exp-sum_binary64` `exp-prod_binary64`
2×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 112

Calls

4 calls:

13.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
18.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
20.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
14.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))) 3))

series320.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))))
57.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
59.0ms	(+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b)))
103.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 (.f64 y (-.f64 (log.f64 z) t)) (.f64 a (-.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 z 1.0) (.f64 1/2 (/.f64 (.f64 z z) (.f64 1.0 1.0))))) b))))) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5191	4432

prune318.0ms

Filtered

100 candidates to 124 candidates (-24.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

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

Merged error: 0.0b

Counts

129 → 5

regimes545.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	114	30
1	114	30

end0.0ms

sample3.0s

Algorithm

intervals

Results

818.0ms	10556×	body	80	nan
575.0ms	7242×	body	80	valid
421.0ms	5352×	body	80	invalid
110.0ms	264×	body	640	valid
69.0ms	255×	body	320	valid
51.0ms	123×	body	640	invalid
39.0ms	48×	body	1280	valid
32.0ms	191×	body	160	valid
30.0ms	116×	body	320	invalid
15.0ms	90×	body	160	invalid
13.0ms	16×	body	1280	invalid

Details

analyze854.0ms

sample100.0ms

simplify46.0ms

prune14.0ms

localize15.0ms

rewrite44.0ms

series133.0ms

simplify77.0ms

prune139.0ms

localize21.0ms

rewrite65.0ms

series245.0ms

simplify82.0ms

prune169.0ms

localize37.0ms

rewrite68.0ms

series327.0ms

simplify59.0ms

prune302.0ms

localize27.0ms

rewrite71.0ms

series320.0ms

simplify56.0ms

prune318.0ms

regimes545.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.0s

Profiling