Details

sample78.0ms

Algorithm

intervals

Results

41.0ms

619×

body

valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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: 12.5b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c a) (* y i))
5.1b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.1b	(* x (- (* y z) (* t a)))
5.2b	(* 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	(- (* c a) (* y i))
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)))

series801.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c a) (* y i))
613.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
74.0ms	(* x (- (* y z) (* t a)))
74.0ms	(* b (- (* c z) (* t i)))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	426	646
1	1675	568
2	5002	568

prune483.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	16	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	80	16	96

Merged error: 4.2b

Counts

96 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
3.1b	(* (cbrt b) (- (* c z) (* t i)))
5.1b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
5.1b	(* x (- (* y z) (* t a)))

rewrite30.0ms

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:

13.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
7.0ms	(* (cbrt b) (- (* c z) (* t i)))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
6.0ms	(* x (- (* y z) (* t a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
298.0ms	(* (cbrt b) (- (* c z) (* t i)))
723.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
76.0ms	(* x (- (* y z) (* t a)))

simplify86.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	563	1204
1	2492	956
2	5001	877

prune568.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	119	17	136

Merged error: 4.2b

Counts

136 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

5.1b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* t (* i b))))))
5.1b	(* x (- (* y z) (* t a)))
5.3b	(* z (* b c))
5.4b	(* t (* i b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
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×	`flip3--` `flip--` `fma-udef` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

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

series742.0ms

Counts

4 → 12

Calls

4 calls:

610.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* t (* i b))))))
77.0ms	(* x (- (* y z) (* t a)))
27.0ms	(* z (* b c))
28.0ms	(* t (* i b))

simplify67.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	378	544
1	1429	461
2	5002	461

prune452.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	89	18	107

Merged error: 4.2b

Counts

107 → 18

localize34.0ms

Local error

Found 4 expressions with local error:

5.1b	(* x (fma y z (- (* a t))))
5.3b	(* z (* b c))
5.4b	(* t (* i b))
49.9b	(fma (- a) t (* a t))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

4.0ms	(* x (fma y z (- (* a t))))
5.0ms	(* z (* b c))
5.0ms	(* t (* i b))
1.0ms	(fma (- a) t (* a t))

series173.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (fma y z (- (* a t))))
28.0ms	(* z (* b c))
35.0ms	(* t (* i b))
29.0ms	(fma (- a) t (* a t))

simplify124.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	283	344
1	1069	287
2	4217	287
3	5001	283

prune411.0ms

Filtered

84 candidates to 56 candidates (66.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	84	18	102

Merged error: 4.2b

Counts

102 → 18

regimes1.2s

Accuracy

22.5% (5.9b remaining)

Error of 10.3b against oracle of 4.4b and baseline of 12.0b

bsearch110.0ms

Steps

Iters	Range		Point
7	6.576768261339047e+96	5.927628932675884e+98	6.685979239250011e+96

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	39
1	62	39
2	62	39

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s

18951×

body

valid