Details

analyze1.3s

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
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

sample27.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	6×	body	80	invalid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	46	17
1	46	17

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: 14.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
6.1b	(/.f64 (*.f64 y b) t)
6.9b	(/.f64 (*.f64 y z) t)
9.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
22×	`distribute-lft-out_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
5.0ms	(/.f64 (*.f64 y b) t)
5.0ms	(/.f64 (*.f64 y z) t)
13.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
6.0ms	(/.f64 (*.f64 y b) t)
8.0ms	(/.f64 (*.f64 y z) t)
46.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5082	1595

prune184.0ms

Filtered

72 candidates to 113 candidates (-56.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	15	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	15	114

Merged error: 8.7b

Counts

114 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
3.7b	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
6.1b	(/.f64 (*.f64 y b) t)
9.1b	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (/.f64 (*.f64 y b) t)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
34×	`add-exp-log_binary64`
33×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`add-cbrt-cube_binary64`
24×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out_binary64`
14×	`associate-/r*_binary64`
11×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
2×	`frac-add_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

10.0ms	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
9.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
5.0ms	(/.f64 (*.f64 y b) t)
15.0ms	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (/.f64 (*.f64 y b) t)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
40.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
6.0ms	(/.f64 (*.f64 y b) t)
86.0ms	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (/.f64 (*.f64 y b) t)))

simplify36.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5334	1916

prune163.0ms

Filtered

92 candidates to 140 candidates (-52.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	141	14	155

Merged error: 8.2b

Counts

155 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
2.8b	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
3.7b	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
9.1b	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
50×	`add-exp-log_binary64` `times-frac_binary64`
43×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
25×	`associate-r_binary64`
17×	`cbrt-prod_binary64`
16×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
14×	`associate-l_binary64`
9×	`associate-/r*_binary64`
8×	`pow1_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
6×	`frac-add_binary64`
5×	`flip3-+_binary64` `associate-/l_binary64` `div-inv_binary64` `flip-+_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64`
3×	`associate-/l/_binary64` `associate-*r/_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

10.0ms	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
14.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
9.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
16.0ms	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))
14.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
45.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z)
103.0ms	(/.f64 (+.f64 x (/.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) z) (cbrt.f64 t))) (+.f64 (+.f64 a 1.0) (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5099	2404

prune187.0ms

Filtered

126 candidates to 172 candidates (-36.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	172	14	186

Merged error: 8.2b

Counts

186 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (/.f64 y t) z))
4.8b	(*.f64 (/.f64 y t) z)
6.1b	(/.f64 (*.f64 y b) t)
9.1b	(/.f64 (+.f64 x (.f64 (/.f64 y t) z)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
12×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

3.0ms	(+.f64 x (*.f64 (/.f64 y t) z))
6.0ms	(*.f64 (/.f64 y t) z)
4.0ms	(/.f64 (*.f64 y b) t)
11.0ms	(/.f64 (+.f64 x (.f64 (/.f64 y t) z)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 x (*.f64 (/.f64 y t) z))
6.0ms	(*.f64 (/.f64 y t) z)
6.0ms	(/.f64 (*.f64 y b) t)
74.0ms	(/.f64 (+.f64 x (.f64 (/.f64 y t) z)) (+.f64 (+.f64 a 1.0) (/.f64 (.f64 y b) t)))

simplify28.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5105	1517

prune89.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	10	12
Picked	1	0	1
Done	1	0	1
Total	119	12	131

Merged error: 8.2b

Counts

131 → 12

regimes801.0ms

Accuracy

17.8% (3.5b remaining)

Error of 13.7b against oracle of 10.2b and baseline of 14.5b

bsearch44.0ms

Steps

Iters	Range		Point
7	6.734230674045045e-140	1.3469265749450483e-138	1.3583837970033708e-139
10	-8.603742217837876e-84	-5.787207828469491e-99	-2.642073336958404e-86

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	47
1	144	47

end0.0ms

sample745.0ms

Algorithm

intervals

Results

438.0ms	8000×	body	80	valid
15.0ms	285×	body	80	invalid

Details

analyze1.3s

sample27.0ms

simplify6.0ms

prune4.0ms

localize16.0ms

rewrite31.0ms

series70.0ms

simplify45.0ms

prune184.0ms

localize19.0ms

rewrite43.0ms

series145.0ms

simplify36.0ms

prune163.0ms

localize17.0ms

rewrite55.0ms

series174.0ms

simplify42.0ms

prune187.0ms

localize11.0ms

rewrite28.0ms

series99.0ms

simplify28.0ms

prune89.0ms

regimes801.0ms

bsearch44.0ms

simplify3.0ms

end0.0ms

sample745.0ms

Profiling