Details

analyze1.7s

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

sample69.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
17.0ms	188×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5545	33

prune5.0ms

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: 5.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.3b	(/.f64 2.0 (*.f64 t 3.0))
2.9b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
5.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `times-frac_binary64`
5×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`associate-/r_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `sqrt-div_binary64`
3×	`sub-neg_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_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 → 98

Calls

4 calls:

7.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
5.0ms	(/.f64 2.0 (*.f64 t 3.0))
13.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series137.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2.0 (*.f64 t 3.0))
82.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (/.f64 2.0 (*.f64 t 3.0)))))
35.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify57.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4965	2272
1	4965	2272

prune208.0ms

Filtered

87 candidates to 110 candidates (-26.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 0.3b

Counts

111 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.3b	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
2.9b	(-.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 (/.f64 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))

rewrite56.0ms

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)
1.0ms	(cbrt.f64 t)
25.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
20.0ms	(-.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 (/.f64 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 t)
17.0ms	(cbrt.f64 t)
26.0ms	(.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
72.0ms	(-.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 (/.f64 5.0 6.0)) (/.f64 2.0 (.f64 t 3.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	5661

prune353.0ms

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: 0.3b

Counts

182 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2.0 (*.f64 t 3.0))
2.0b	(log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0))))
5.6b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0)))))))
5.6b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
8×	`log-pow_binary64` `frac-sub_binary64`
7×	`flip3--_binary64` `flip--_binary64` `exp-prod_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/r_binary64` `associate--r+_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/l*_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `log-prod_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64` `associate--l+_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `rem-log-exp_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

4 calls:

5.0ms	(/.f64 2.0 (*.f64 t 3.0))
4.0ms	(log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0))))
14.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0)))))))
8.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series94.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 2.0 (*.f64 t 3.0))
3.0ms	(log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0))))
66.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5.0 6.0)) (log.f64 (exp.f64 (/.f64 2.0 (*.f64 t 3.0)))))))
22.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

simplify37.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5035	1665

prune144.0ms

Filtered

79 candidates to 98 candidates (-24.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0.3b

Counts

102 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 c (+.f64 a 0.8333333333333334))
0.0b	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
0.2b	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
0.9b	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`associate-r_binary64`
12×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `exp-sum_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `associate--l+_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`associate-l_binary64`
5×	`sub-neg_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `flip--_binary64` `exp-to-pow_binary64` `flip-+_binary64` `exp-prod_binary64`

Counts

4 → 76

Calls

4 calls:

7.0ms	(*.f64 c (+.f64 a 0.8333333333333334))
5.0ms	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
8.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
7.0ms	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

series62.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 c (+.f64 a 0.8333333333333334))
15.0ms	(exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (*.f64 a b))))
29.0ms	(.f64 y (exp.f64 (.f64 2.0 (-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b)))))
12.0ms	(-.f64 (.f64 c (+.f64 a 0.8333333333333334)) (.f64 a b))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4997	970
1	4997	970

prune79.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	88	4	92

Merged error: 0.2b

Counts

92 → 4

regimes650.0ms

Accuracy

33% (1.6b remaining)

Error of 1.9b against oracle of 0.3b and baseline of 2.6b

bsearch122.0ms

Steps

Iters	Range		Point
9	2.014720174304216e-127	7.1248934196325385e-118	2.5292981124674526e-127
9	-1.0691380559601449e-142	-1.755014413416689e-148	-3.433275005074214e-144

simplify17.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	866	116
1	866	116

end0.0ms

sample1.8s

Algorithm

intervals

Results

776.0ms	8000×	body	80	valid
485.0ms	5147×	body	80	nan

Details

analyze1.7s

sample69.0ms

simplify36.0ms

prune5.0ms

localize22.0ms

rewrite37.0ms

series137.0ms

simplify57.0ms

prune208.0ms

localize27.0ms

rewrite56.0ms

series133.0ms

simplify64.0ms

prune353.0ms

localize27.0ms

rewrite34.0ms

series94.0ms

simplify37.0ms

prune144.0ms

localize14.0ms

rewrite30.0ms

series62.0ms

simplify48.0ms

prune79.0ms

regimes650.0ms

bsearch122.0ms

simplify17.0ms

end0.0ms

sample1.8s

Profiling