Details

analyze1.2s

Algorithm

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
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

sample112.0ms

Algorithm

intervals

Results

29.0ms	47×	body	1280	valid
21.0ms	60×	body	640	valid
10.0ms	7×	body	2560	valid
8.0ms	105×	body	80	valid
5.0ms	23×	body	320	valid
5.0ms	17×	body	640	nan
3.0ms	9×	body	1280	nan
2.0ms	36×	body	80	nan
2.0ms	14×	body	160	valid
1.0ms	26×	body	80	overflowed
1.0ms	8×	body	320	nan

simplify325.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (316.0ms)

Iter	Nodes	Cost
0	5254	20

prune11.0ms

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: 27.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.1b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
2.4b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
3.4b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_3769`
16×	`*-un-lft-identity_binary64_3784` `add-cube-cbrt_binary64_3755`
12×	`times-frac_binary64_3779`
11×	`pow1_binary64_3730`
9×	`add-log-exp_binary64_3749`
8×	`add-exp-log_binary64_3748` `add-cbrt-cube_binary64_3756`
5×	`log-pow_binary64_3705`
4×	`associate-/l*_binary64_3848` `log-div_binary64_3703`
3×	`associate-l_binary64_3844` `associate-/r_binary64_3847` `log-prod_binary64_3702` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-r*_binary64_3843`
2×	`div-sub_binary64_3778` `sum-log_binary64_3699`
1×	`+-commutative_binary64_3851` `*-commutative_binary64_3852` `clear-num_binary64_3787` `rem-log-exp_binary64_3747` `cbrt-unprod_binary64_3753` `prod-exp_binary64_3735` `frac-2neg_binary64_3777` `associate-+l-_binary64_3838` `pow-prod-down_binary64_3711` `div-inv_binary64_3785` `unswap-sqr_binary64_3812` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737` `diff-log_binary64_3700` `associate-+l+_binary64_3836` `sub-neg_binary64_3788`

Counts

4 → 79

Calls

4 calls:

5.0ms	(*.f64 y (exp.f64 z))
9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
6.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
7.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 y (exp.f64 z))
185.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
64.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
29.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

simplify70.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5447	1971

prune397.0ms

Filtered

70 candidates to 91 candidates (-30.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 5.3b

Counts

92 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
3.5b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.3b	(.f64 y (.f64 z z))
7.8b	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log_binary64_3748` `add-cbrt-cube_binary64_3756`
23×	`pow1_binary64_3730`
18×	`add-sqr-sqrt_binary64_3769`
17×	`*-un-lft-identity_binary64_3784`
14×	`add-cube-cbrt_binary64_3755`
13×	`cbrt-unprod_binary64_3753` `prod-exp_binary64_3735` `pow-prod-down_binary64_3711`
9×	`times-frac_binary64_3779`
7×	`associate-r_binary64_3843`
6×	`add-log-exp_binary64_3749`
4×	`associate-l_binary64_3844` `sub-neg_binary64_3788`
3×	`associate-/r_binary64_3847` `associate-/l_binary64_3848`
2×	`-commutative_binary64_3852` `associate-/l/_binary64_3850` `difference-of-squares_binary64_3813` `distribute-lft-in_binary64_3826` `associate-+r+_binary64_3835` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-r/_binary64_3845` `distribute-rgt-in_binary64_3827`
1×	`+-commutative_binary64_3851` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `distribute-lft-out--_binary64_3829` `div-inv_binary64_3785` `flip3--_binary64_3783` `unswap-sqr_binary64_3812` `flip--_binary64_3810` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737` `sum-log_binary64_3699`

Counts

4 → 92

Calls

4 calls:

6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
13.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.0ms	(.f64 y (.f64 z z))
8.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

series215.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
48.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
26.0ms	(.f64 y (.f64 z z))
90.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)

simplify83.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5548	2260

prune406.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 5.2b

Counts

113 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
3.5b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.3b	(.f64 y (.f64 z z))
7.8b	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64_3748`
28×	`add-cbrt-cube_binary64_3756`
25×	`pow1_binary64_3730` `add-sqr-sqrt_binary64_3769`
20×	`associate-r_binary64_3843`
18×	`*-un-lft-identity_binary64_3784`
16×	`prod-exp_binary64_3735`
15×	`cbrt-unprod_binary64_3753`
14×	`pow-prod-down_binary64_3711` `add-cube-cbrt_binary64_3755`
11×	`times-frac_binary64_3779`
7×	`associate-l_binary64_3844`
6×	`add-log-exp_binary64_3749`
4×	`unswap-sqr_binary64_3812` `sub-neg_binary64_3788`
3×	`-commutative_binary64_3852` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-r/_binary64_3845`
2×	`associate-*l/_binary64_3846` `difference-of-squares_binary64_3813` `frac-times_binary64_3776` `distribute-lft-in_binary64_3826` `associate-+r+_binary64_3835` `distribute-rgt-in_binary64_3827`
1×	`un-div-inv_binary64_3786` `+-commutative_binary64_3851` `distribute-lft-out--_binary64_3829` `div-inv_binary64_3785` `flip3--_binary64_3783` `flip--_binary64_3810` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737` `rec-exp_binary64_3736` `sum-log_binary64_3699`

Counts

4 → 102

Calls

4 calls:

6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
13.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
6.0ms	(.f64 y (.f64 z z))
11.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

series217.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
49.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
30.0ms	(.f64 y (.f64 z z))
92.0ms	(.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))) (/.f64 1 t))

simplify88.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	6010	2431

prune420.0ms

Filtered

70 candidates to 114 candidates (-62.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	112	15	127

Merged error: 5.2b

Counts

127 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
2.6b	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))
3.7b	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))
7.8b	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac_binary64_3779`
35×	`add-exp-log_binary64_3748`
32×	`add-sqr-sqrt_binary64_3769`
30×	`*-un-lft-identity_binary64_3784`
29×	`add-cbrt-cube_binary64_3756`
27×	`add-cube-cbrt_binary64_3755`
16×	`pow1_binary64_3730`
12×	`associate-*r/_binary64_3845`
11×	`associate-/r/_binary64_3849`
10×	`prod-exp_binary64_3735` `associate-/r*_binary64_3847`
9×	`cbrt-unprod_binary64_3753` `associate-l_binary64_3844` `div-exp_binary64_3737`
7×	`pow-prod-down_binary64_3711` `cbrt-undiv_binary64_3754`
6×	`div-inv_binary64_3785` `associate-/l*_binary64_3848` `flip-+_binary64_3809` `flip3-+_binary64_3782`
4×	`add-log-exp_binary64_3749` `associate-r_binary64_3843`
3×	`rec-exp_binary64_3736`
2×	`-commutative_binary64_3852` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-l/_binary64_3846` `difference-of-squares_binary64_3813`
1×	`inv-pow_binary64_3706` `distribute-lft-out--_binary64_3829` `flip3--_binary64_3783` `distribute-lft-in_binary64_3826` `unswap-sqr_binary64_3812` `flip--_binary64_3810` `pow-flip_binary64_3714` `distribute-rgt-in_binary64_3827`

Counts

4 → 132

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
6.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))
11.0ms	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))
7.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))))
57.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z)))))
41.0ms	(.f64 (-.f64 1 y) (.f64 1/2 (*.f64 z z)))
151.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 1/2 (.f64 z z))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4945	3794
1	4945	3794

prune467.0ms

Filtered

97 candidates to 144 candidates (-48.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	146	13	159

Merged error: 3.3b

Counts

159 → 13

regimes915.0ms

Accuracy

46.2% (5.4b remaining)

Error of 8.6b against oracle of 3.2b and baseline of 13.2b

bsearch2.0ms

simplify11.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	316	68
1	316	68

end0.0ms

sample2.8s

Algorithm

intervals

Results

898.0ms	1493×	body	1280	valid
538.0ms	1523×	body	640	valid
268.0ms	3535×	body	80	valid
200.0ms	886×	body	320	valid
160.0ms	116×	body	2560	valid
75.0ms	1497×	body	80	nan
73.0ms	296×	body	640	nan
63.0ms	447×	body	160	valid
46.0ms	822×	body	80	overflowed
42.0ms	113×	body	1280	nan
34.0ms	187×	body	320	nan
13.0ms	120×	body	160	nan
1.0ms	17×	body	80	invalid
1.0ms	4×	body	320	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.2s

sample112.0ms

simplify325.0ms

prune11.0ms

localize15.0ms

rewrite29.0ms

series300.0ms

simplify70.0ms

prune397.0ms

localize19.0ms

rewrite35.0ms

series215.0ms

simplify83.0ms

prune406.0ms

localize23.0ms

rewrite39.0ms

series217.0ms

simplify88.0ms

prune420.0ms

localize21.0ms

rewrite38.0ms

series377.0ms

simplify74.0ms

prune467.0ms

regimes915.0ms

bsearch2.0ms

simplify11.0ms

end0.0ms

sample2.8s

Profiling