Details

analyze1.9s

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
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

sample74.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
21.0ms	167×	body	80	nan

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4938	29
1	4938	29

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b	(/.f64 2/3 t)
2.0b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
4.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
20×	`frac-sub_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`times-frac_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
5×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`associate--r+_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms	(/.f64 2/3 t)
20.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series99.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)
61.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
21.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4951	1974
1	4951	1974

prune183.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 0.2b

Counts

117 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 t)
0.7b	(cbrt.f64 t)
2.0b	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
3.0b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
60×	`frac-sub_binary64`
58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
46×	`associate-r_binary64`
39×	`frac-times_binary64`
35×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`
28×	`sqrt-prod_binary64`
27×	`associate-*r/_binary64`
25×	`flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
21×	`associate-*l/_binary64`
18×	`add-cbrt-cube_binary64`
10×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`associate--r+_binary64`
3×	`sub-neg_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

1.0ms	(cbrt.f64 t)
2.0ms	(cbrt.f64 t)
24.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 t)
15.0ms	(cbrt.f64 t)
67.0ms	(-.f64 (.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

simplify53.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4992	4847
1	4992	4847

prune309.0ms

Filtered

141 candidates to 178 candidates (-26.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Merged error: 0.2b

Counts

182 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
3.4b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
3.6b	(log.f64 (exp.f64 (/.f64 2/3 t)))
4.0b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
14×	`log-pow_binary64`
13×	`exp-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`frac-sub_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate--r+_binary64` `associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `flip-+_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(/.f64 2/3 t)
14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
5.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series87.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 2/3 t)
56.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
2.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
25.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify61.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4952	1504
1	4952	1504

prune154.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.2b

Counts

114 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

3.6b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
5.5b	(.f64 t (-.f64 (.f64 a a) 25/36))
6.0b	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
25.6b	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

1530×	`associate-*r/_binary64`
768×	`frac-sub_binary64`
713×	`flip3--_binary64` `flip--_binary64`
528×	`frac-times_binary64`
360×	`sqrt-div_binary64`
180×	`flip3-+_binary64` `flip-+_binary64`
168×	`associate-*l/_binary64`
162×	`associate-/l/_binary64`
29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`sub-neg_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`associate--l+_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 577

Calls

4 calls:

35.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
9.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))
47.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
70.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
11.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))
236.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
269.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

simplify259.0ms

Algorithm

egg-herbie

Counts

589 → 589

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5386	41334

prune7.2s

Filtered

563 candidates to 589 candidates (-4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	588	1	589
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	589	4	593

Merged error: 0.0b

Counts

593 → 4

regimes714.0ms

Accuracy

-4.1% (2.2b remaining)

Error of 2.6b against oracle of 0.3b and baseline of 2.5b

bsearch186.0ms

Steps

Iters	Range		Point
8	2.3310241609612174e-307	7.861992104542329e-303	1.1020250707256974e-304
10	-2.94203197036526e+39	-6.653045874546673e+24	-6.768047101784082e+24

simplify21.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	754	94
1	754	94

end0.0ms

sample1.9s

Algorithm

intervals

Results

796.0ms	8000×	body	80	valid
476.0ms	4926×	body	80	nan

Details

analyze1.9s

sample74.0ms

simplify28.0ms

prune13.0ms

localize25.0ms

rewrite45.0ms

series99.0ms

simplify66.0ms

prune183.0ms

localize30.0ms

rewrite68.0ms

series124.0ms

simplify53.0ms

prune309.0ms

localize26.0ms

rewrite36.0ms

series87.0ms

simplify61.0ms

prune154.0ms

localize36.0ms

rewrite281.0ms

series668.0ms

simplify259.0ms

prune7.2s

regimes714.0ms

bsearch186.0ms

simplify21.0ms

end0.0ms

sample1.9s

Profiling