Details

sample76.0ms

Algorithm

intervals

Results

40.0ms

623×

body

valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

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: 10.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* y z) (* t a))
3.9b	(* b (- (* c z) (* i a)))
4.1b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.1b	(* x (- (* y z) (* t a)))

rewrite18.0ms

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

series726.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* y z) (* t a))
69.0ms	(* b (- (* c z) (* i a)))
552.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
66.0ms	(* x (- (* y z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	373	645
1	1485	568
2	5001	568

prune392.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 5.1b

Counts

95 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

3.9b	(* b (- (* c z) (* i a)))
4.1b	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
6.1b	(* x (fma y z (- (* a t))))
49.4b	(fma (- a) t (* a t))

rewrite13.0ms

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:

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

series3.5s

Counts

4 → 12

Calls

4 calls:

75.0ms	(* b (- (* c z) (* i a)))
3.4s	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
72.0ms	(* x (fma y z (- (* a t))))
26.0ms	(fma (- a) t (* a t))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	315	624
1	1247	538
2	5002	538

prune384.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 5.1b

Counts

95 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

3.9b	(* b (- (* c z) (* i a)))
4.1b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
6.1b	(* x (- (* y z) (* t a)))
51.6b	(fma (- a) i (* a i))

rewrite16.0ms

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:

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

series3.8s

Counts

4 → 12

Calls

4 calls:

69.0ms	(* b (- (* c z) (* i a)))
3.6s	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
70.0ms	(* x (- (* y z) (* t a)))
33.0ms	(fma (- a) i (* a i))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	360	664
1	1457	577
2	5002	577

prune413.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	89	11	100

Merged error: 5.1b

Counts

100 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

4.1b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.1b	(* x (- (* y z) (* t a)))
6.1b	(* x (- (* y z) (* t a)))
6.1b	(* x (- (* y z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

906.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
85.0ms	(* x (- (* y z) (* t a)))
81.0ms	(* x (- (* y z) (* t a)))
75.0ms	(* x (- (* y z) (* t a)))

simplify105.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	221	738
1	799	648
2	3102	648
3	5002	648

prune531.0ms

Filtered

106 candidates to 81 candidates (76.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 5.1b

Counts

117 → 12

regimes748.0ms

Accuracy

6.2% (7.3b remaining)

Error of 12.6b against oracle of 5.4b and baseline of 13.1b

bsearch175.0ms

Steps

Iters	Range		Point
10	1.6341238352621664e+152	1.1968141550214114e+170	1.986175582965001e+163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	56
1	58	56

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

19107×

body

valid