Details

sample91.0ms

Algorithm

intervals

Results

53.0ms

629×

body

valid

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 12.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c a) (* y i))
4.4b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.8b	(* b (- (* c z) (* t i)))
5.5b	(* x (- (* y z) (* t a)))

rewrite23.0ms

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)))))
9.0ms	(* b (- (* c z) (* t i)))
7.0ms	(* x (- (* y z) (* t a)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* c a) (* y i))
621.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
74.0ms	(* b (- (* c z) (* t i)))
71.0ms	(* x (- (* y z) (* t a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (17.0ms)

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

prune476.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	73	21	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	21	95

Merged error: 5.0b

Counts

95 → 21

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
4.8b	(* b (- (* c z) (* t i)))
5.5b	(* x (fma y z (- (* a t))))
49.4b	(fma (- a) t (* a t))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series3.8s

Counts

4 → 12

Calls

4 calls:

3.6s	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
69.0ms	(* b (- (* c z) (* t i)))
78.0ms	(* x (fma y z (- (* a t))))
28.0ms	(fma (- a) t (* a t))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	310	624
1	1230	538
2	5001	538

prune440.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	83	20	103

Merged error: 5.0b

Counts

103 → 20

localize31.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma (+ (- (* a c) (* i y)) (fma (- i) y (* i y))) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.8b	(* b (- (* c z) (* t i)))
5.5b	(* x (- (* y z) (* t a)))
49.2b	(fma (- i) y (* i y))

rewrite17.0ms

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`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `prod-diff` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

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

series838.0ms

Counts

4 → 12

Calls

4 calls:

659.0ms	(fma (+ (- (* a c) (* i y)) (fma (- i) y (* i y))) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
75.0ms	(* b (- (* c z) (* t i)))
75.0ms	(* x (- (* y z) (* t a)))
28.0ms	(fma (- i) y (* i y))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	364	656
1	1448	572
2	5002	572

prune442.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	89	19	108

Merged error: 5.0b

Counts

108 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (cbrt b) (- (* c z) (* t i)))
3.2b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
4.4b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
5.5b	(* x (- (* y z) (* t a)))

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:

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

series1.3s

Counts

4 → 12

Calls

4 calls:

343.0ms	(* (cbrt b) (- (* c z) (* t i)))
110.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
724.0ms	(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)))

simplify107.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (86.0ms)

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

prune468.0ms

Filtered

120 candidates to 80 candidates (66.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	119	20	139

Merged error: 4.8b

Counts

139 → 20

regimes1.3s

Accuracy

42.8% (4.5b remaining)

Error of 8.7b against oracle of 4.2b and baseline of 12.1b

bsearch216.0ms

Steps

Iters	Range		Point
8	2454864494654.6284	1057652120957756.5	449011503178547.75
6	-262084320804.18658	-31770318212.664288	-153741547584.47736

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	55
1	72	55
2	72	55

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.8s

19100×

body

valid