Details

sample74.0ms

Algorithm

intervals

Results

39.0ms

617×

body

valid

simplify86.0ms

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

prune8.0ms

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: 10.8b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c t) (* i y))
3.0b	(* x (- (* y z) (* t a)))
4.3b	(* b (- (* c z) (* i a)))
5.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i 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:

3.0ms	(- (* c t) (* i y))
6.0ms	(* x (- (* 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)))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c t) (* i y))
69.0ms	(* x (- (* y z) (* t a)))
63.0ms	(* b (- (* c z) (* i a)))
523.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	423	646
1	1659	568
2	5001	568

prune429.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	76	18	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	18	95

Merged error: 3.9b

Counts

95 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b	(* x (- (* y z) (* t a)))
4.3b	(* b (- (* c z) (* i a)))
5.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
49.9b	(fma (- a) i (* a i))

rewrite15.0ms

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	(* x (- (* 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))) (* b (fma (- a) i (* a i))))))
1.0ms	(fma (- a) i (* a i))

series3.7s

Counts

4 → 12

Calls

4 calls:

71.0ms	(* x (- (* y z) (* t a)))
78.0ms	(* 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))))))
28.0ms	(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

prune499.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	9	8	17
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 3.9b

Counts

106 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (- (* y z) (* t a)))
4.9b	(cbrt (- (* y z) (* t a)))
5.0b	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
49.9b	(fma (- a) i (* a i))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `pow1/3` `flip--` `fma-udef`

Counts

4 → 50

Calls

4 calls:

3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
1.0ms	(fma (- a) i (* a i))

series3.9s

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (- (* y z) (* t a)))
133.0ms	(cbrt (- (* y z) (* t a)))
3.6s	(fma (- (* c t) (* i y)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
28.0ms	(fma (- a) i (* a i))

simplify75.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	288	736
1	783	651
2	2540	623
3	5001	614

prune504.0ms

Filtered

62 candidates to 55 candidates (88.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	63	15	78

Merged error: 3.9b

Counts

78 → 15

localize39.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
4.3b	(* b (- (* c z) (* i a)))
5.0b	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
49.9b	(fma (- a) i (* a i))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

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

series4.2s

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
79.0ms	(* b (- (* c z) (* i a)))
4.0s	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
30.0ms	(fma (- a) i (* a i))

simplify67.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	491	1060
1	1875	810
2	5001	735

prune402.0ms

Filtered

98 candidates to 59 candidates (60.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Merged error: 3.9b

Counts

113 → 15

regimes875.0ms

Accuracy

3.4% (7.9b remaining)

Error of 12.3b against oracle of 4.4b and baseline of 12.6b

bsearch151.0ms

Steps

Iters	Range		Point
9	-4.450874028495172e+227	-2.009354561924679e+220	-1.1558946599151163e+223

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	30
1	54	30

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19292×

body

valid