Details

analyze899.0ms

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

sample273.0ms

Algorithm

intervals

Results

82.0ms	116×	body	1280	valid
60.0ms	96×	body	1280	nan
41.0ms	83×	body	640	valid
38.0ms	85×	body	640	nan
19.0ms	45×	body	320	nan
12.0ms	34×	body	320	valid
4.0ms	18×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	5×	body	80	valid

simplify453.0ms

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: 62.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4.0) f)
0.3b	(*.f64 (/.f64 PI.f64 4.0) f)
1.2b	(/.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)))))
4.8b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out_binary64` `sinh-undef_binary64` `cosh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r*_binary64`
5×	`associate-/l*_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 135

Calls

4 calls:

7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
7.0ms	(*.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)))))
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
34.0ms	(/.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)))))
20.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

simplify69.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5384	3034

prune268.0ms

Filtered

110 candidates to 147 candidates (-33.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 2.0b

Counts

148 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4.0) f)
0.3b	(*.f64 (/.f64 PI.f64 4.0) f)
0.4b	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
1.4b	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac_binary64`
97×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
70×	`associate-l_binary64`
28×	`log-prod_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64`
9×	`div-inv_binary64`
7×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `sinh-def_binary64` `associate-/l_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-/l/_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `cosh-def_binary64`

Counts

4 → 188

Calls

4 calls:

7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
16.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
5.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
77.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
40.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

simplify64.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5002	3817

prune314.0ms

Filtered

154 candidates to 200 candidates (-29.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	196	7	203

Merged error: 1.5b

Counts

203 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4.0) f)
0.3b	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))))
0.3b	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
1.4b	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

154×	`times-frac_binary64`
109×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
91×	`sqrt-prod_binary64`
64×	`associate-l_binary64`
51×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`pow1_binary64`
10×	`div-inv_binary64`
6×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`associate-/r_binary64` `associate-/r/_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`associate-/l/_binary64` `sinh-def_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `cosh-def_binary64`

Counts

4 → 193

Calls

4 calls:

7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
19.0ms	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))))
22.0ms	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
5.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 (/.f64 PI.f64 4.0) f)
80.0ms	(.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))))
86.0ms	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
37.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))

simplify80.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4967	4422
1	4967	4422

prune406.0ms

Filtered

168 candidates to 205 candidates (-22.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	206	6	212

Merged error: 1.5b

Counts

212 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
1.3b	(log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
1.3b	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f))))
1.6b	(/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

594×	`times-frac_binary64`
319×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
314×	`sqrt-prod_binary64`
143×	`log-prod_binary64`
47×	`associate-l_binary64`
26×	`associate-/l*_binary64`
22×	`add-exp-log_binary64`
20×	`div-inv_binary64` `sqrt-div_binary64`
17×	`associate-/r/_binary64`
16×	`sinh-def_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r*_binary64`
10×	`pow1_binary64`
7×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-r_binary64` `log-pow_binary64` `log-div_binary64` `frac-times_binary64` `cosh-def_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 444

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
17.0ms	(log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
6.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f))))
13.0ms	(/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0))) (.f64 (log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))) (sqrt.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)))))
62.0ms	(log.f64 (/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f)))))
38.0ms	(/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f))))
42.0ms	(/.f64 (/.f64 (cosh.f64 (.f64 (/.f64 PI.f64 4.0) f)) (sqrt.f64 (sinh.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (sqrt.f64 (sinh.f64 (*.f64 (/.f64 PI.f64 4.0) f))))

simplify133.0ms

Algorithm

egg-herbie

Counts

456 → 456

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4970	15664
1	4970	15664

prune750.0ms

Filtered

232 candidates to 456 candidates (-96.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	453	3	456
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	454	8	462

Merged error: 1.5b

Counts

462 → 8

regimes100.0ms

Accuracy

0% (0.5b remaining)

Error of 2.0b against oracle of 1.5b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	30
1	47	30

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.3s	3529×	body	1280	valid
1.8s	2946×	body	1280	nan
1.1s	2385×	body	640	valid
1.1s	2443×	body	640	nan
426.0ms	1201×	body	320	valid
405.0ms	1227×	body	320	nan
158.0ms	640×	body	160	valid
52.0ms	231×	body	160	nan
30.0ms	245×	body	80	valid
1.0ms	5×	body	80	overflowed

Details

analyze899.0ms

sample273.0ms

simplify453.0ms

prune4.0ms

localize26.0ms

rewrite40.0ms

series63.0ms

simplify69.0ms

prune268.0ms

localize11.0ms

rewrite46.0ms

series125.0ms

simplify64.0ms

prune314.0ms

localize13.0ms

rewrite63.0ms

series207.0ms

simplify80.0ms

prune406.0ms

localize16.0ms

rewrite88.0ms

series224.0ms

simplify133.0ms

prune750.0ms

regimes100.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.6s

Profiling