Details

sample97.0ms

Algorithm

intervals

Results

55.0ms

634×

body

valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 12.9b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y z) (* t a))
4.2b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.9b	(* x (- (* y z) (* t a)))
5.9b	(* b (- (* c z) (* t i)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* y z) (* t a))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* t i)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* y z) (* t a))
604.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
74.0ms	(* x (- (* y z) (* t a)))
75.0ms	(* b (- (* c z) (* t i)))

simplify63.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	376	645
1	1500	568
2	5001	568

prune412.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 4.5b

Counts

96 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

4.2b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* t i))))))
4.4b	(* b (* c z))
4.9b	(* x (- (* y z) (* t a)))
7.1b	(* b (- (* t i)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
10×	`associate-r`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `associate-*r/` `prod-diff` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `flip3--` `distribute-rgt-neg-in` `distribute-rgt-neg-out` `flip--` `fma-udef`

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* t i))))))
5.0ms	(* b (* c z))
6.0ms	(* x (- (* y z) (* t a)))
7.0ms	(* b (- (* t i)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

597.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* t i))))))
25.0ms	(* b (* c z))
72.0ms	(* x (- (* y z) (* t a)))
27.0ms	(* b (- (* t i)))

simplify67.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	385	576
1	1768	498
2	5002	495

prune382.0ms

Filtered

94 candidates to 70 candidates (74.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 4.5b

Counts

106 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

4.2b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- t)) i))))
4.3b	(* (* b (- t)) i)
4.4b	(* b (* c z))
4.9b	(* x (- (* y z) (* t a)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `associate-*r/` `prod-diff`
1×	`distribute-lft-neg-out` `flip3--` `distribute-rgt-neg-out` `flip--` `fma-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- t)) i))))
6.0ms	(* (* b (- t)) i)
6.0ms	(* b (* c z))
6.0ms	(* x (- (* y z) (* t a)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

604.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- t)) i))))
28.0ms	(* (* b (- t)) i)
25.0ms	(* b (* c z))
73.0ms	(* x (- (* y z) (* t a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	409	569
1	1751	486
2	5001	484

prune351.0ms

Filtered

91 candidates to 64 candidates (70.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	91	11	102

Merged error: 4.5b

Counts

102 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (cbrt x) (- (* y z) (* t a)))
2.9b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
4.2b	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
5.9b	(* b (- (* c z) (* t i)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
18×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sub-neg` `associate-*r/` `prod-diff`
7×	`associate-r`
4×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 108

Calls

4 calls:

8.0ms	(* (cbrt x) (- (* y z) (* t a)))
13.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
1.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
6.0ms	(* b (- (* c z) (* t i)))

series1.2s

Counts

4 → 12

Calls

4 calls:

305.0ms	(* (cbrt x) (- (* y z) (* t a)))
112.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
725.0ms	(fma (- (* c a) (* y i)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (* b (- (* c z) (* t i)))))
74.0ms	(* b (- (* c z) (* t i)))

simplify91.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	557	1206
1	2447	956
2	5003	877

prune420.0ms

Filtered

120 candidates to 77 candidates (64.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	120	11	131

Merged error: 4.5b

Counts

131 → 11

regimes678.0ms

Accuracy

17.7% (6.4b remaining)

Error of 11.3b against oracle of 4.8b and baseline of 12.6b

bsearch247.0ms

Steps

Iters	Range		Point
9	6.096241215763898e-46	4.9291277760064667e-39	2.2411398275451714e-45
7	-6.466699323039071e-109	-3.0683383632404918e-111	-6.340894777041533e-110

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	33
1	66	33
2	70	33
3	70	33

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s

19045×

body

valid