Details

analyze928.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

sample255.0ms

Algorithm

intervals

Results

83.0ms	118×	body	1280	valid
57.0ms	86×	body	1280	nan
32.0ms	64×	body	640	valid
31.0ms	68×	body	640	nan
16.0ms	45×	body	320	nan
12.0ms	34×	body	320	valid
7.0ms	27×	body	160	valid
2.0ms	13×	body	80	valid
1.0ms	6×	body	160	nan

simplify438.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5009	37

prune4.0ms

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: 60.1b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4.0) f)
0.3b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
1.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
6.7b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
36×	`log-prod_binary64`
14×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64` `cosh-undef_binary64` `associate-l_binary64`
12×	`sinh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 150

Calls

4 calls:

7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
12.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
54.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
35.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
21.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

simplify80.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4923	4834
1	4923	4834

prune329.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Merged error: 2.1b

Counts

163 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`
18×	`add-exp-log_binary64`
13×	`log-prod_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`flip3-+_binary64` `flip-+_binary64` `frac-sub_binary64`
7×	`associate-r_binary64`
6×	`pow-unpow_binary64` `associate-*r/_binary64` `unpow-prod-down_binary64` `frac-times_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64`
3×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `pow-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `log-div_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

48.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
3.0ms	(log.f64 (/.f64 4.0 PI.f64))

series28.0ms

Counts

4 → 6

Calls

4 calls:

28.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(log.f64 (/.f64 4.0 PI.f64))

simplify62.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5658	5952

prune446.0ms

Filtered

119 candidates to 150 candidates (-26.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	7	150
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 1.8b

Counts

154 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 f) PI.f64)
0.4b	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
16×	`add-log-exp_binary64`
13×	`log-prod_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`flip3-+_binary64` `diff-log_binary64` `associate-/l*_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`

Counts

4 → 100

Calls

4 calls:

4.0ms	(/.f64 (log.f64 f) PI.f64)
19.0ms	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
2.0ms	(pow.f64 PI.f64 3)
3.0ms	(log.f64 (/.f64 4.0 PI.f64))

series34.0ms

Counts

4 → 8

Calls

4 calls:

12.0ms	(/.f64 (log.f64 f) PI.f64)
22.0ms	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(log.f64 (/.f64 4.0 PI.f64))

simplify41.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5335	2161

prune180.0ms

Filtered

71 candidates to 108 candidates (-52.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Merged error: 1.8b

Counts

118 → 10

localize43.0ms

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
1.6b	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`log-prod_binary64`
11×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `times-frac_binary64`
7×	`pow1_binary64`
6×	`cbrt-prod_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64`
2×	`rem-log-exp_binary64`
1×	`unpow2_binary64` `pow1/3_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 89

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
5.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
2.0ms	(pow.f64 PI.f64 4)
3.0ms	(log.f64 (/.f64 4.0 PI.f64))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(log.f64 (/.f64 4.0 PI.f64))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4914	753
1	4914	753

prune159.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	93	10	103

Merged error: 1.8b

Counts

103 → 10

regimes274.0ms

Accuracy

0% (0.8b remaining)

Error of 2.4b against oracle of 1.7b and baseline of 2.4b

bsearch0.0ms

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	512	33
1	512	33

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.4s	3435×	body	1280	valid
1.8s	2941×	body	1280	nan
1.2s	2467×	body	640	valid
1.1s	2432×	body	640	nan
455.0ms	1255×	body	320	valid
403.0ms	1207×	body	320	nan
147.0ms	592×	body	160	valid
63.0ms	270×	body	160	nan
31.0ms	251×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze928.0ms

sample255.0ms

simplify438.0ms

prune4.0ms

localize28.0ms

rewrite43.0ms

series114.0ms

simplify80.0ms

prune329.0ms

localize30.0ms

rewrite62.0ms

series28.0ms

simplify62.0ms

prune446.0ms

localize27.0ms

rewrite31.0ms

series34.0ms

simplify41.0ms

prune180.0ms

localize43.0ms

rewrite16.0ms

series0.0ms

simplify42.0ms

prune159.0ms

regimes274.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample7.8s

Profiling