Details

sample78.0ms

Algorithm

intervals

Results

41.0ms

607×

body

valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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: 11.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c z) (* t i))
3.0b	(* x (- (* y z) (* t a)))
4.7b	(* b (- (* c z) (* t i)))
5.6b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))

rewrite20.0ms

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

series817.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* c z) (* t i))
78.0ms	(* x (- (* y z) (* t a)))
82.0ms	(* b (- (* c z) (* t i)))
615.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	645
1	1494	568
2	5001	568

prune476.0ms

Filtered

94 candidates to 73 candidates (77.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	80	14	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 5.0b

Counts

95 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

3.0b	(* x (- (* y z) (* t a)))
4.2b	(* b (- (* t i)))
4.3b	(* b (* c z))
5.6b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* t i))))))

rewrite19.0ms

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:

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

series787.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* x (- (* y z) (* t a)))
33.0ms	(* b (- (* t i)))
32.0ms	(* b (* c z))
631.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* t i))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	385	576
1	1763	498
2	5001	495

prune745.0ms

Filtered

94 candidates to 70 candidates (74.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 4.6b

Counts

108 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(* x (fma y z (- (* a t))))
4.7b	(* b (- (* c z) (* t i)))
5.6b	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
49.6b	(fma (- a) t (* a t))

rewrite14.0ms

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:

4.0ms	(* x (fma y z (- (* a t))))
7.0ms	(* b (- (* c z) (* t i)))
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)))))
1.0ms	(fma (- a) t (* a t))

series3.9s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* x (fma y z (- (* a t))))
89.0ms	(* b (- (* c z) (* t i)))
3.7s	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
32.0ms	(fma (- a) t (* a t))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (12.0ms)

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

prune453.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Merged error: 4.6b

Counts

96 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (- (* y z) (* t a)))
4.9b	(cbrt (- (* y z) (* t a)))
4.9b	(cbrt (- (* y z) (* t a)))
5.6b	(fma (- (* c a) (* y i)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (+ (* b (* c z)) (* b (- (* t i))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series900.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (- (* y z) (* t a)))
114.0ms	(cbrt (- (* y z) (* t a)))
124.0ms	(cbrt (- (* y z) (* t a)))
546.0ms	(fma (- (* c a) (* y i)) j (- (* (* x (* (cbrt (- (* y z) (* t a))) (cbrt (- (* y z) (* t a))))) (cbrt (- (* y z) (* t a)))) (+ (* b (* c z)) (* b (- (* t i))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	275	804
1	753	723
2	2271	687
3	5003	682

prune410.0ms

Filtered

67 candidates to 61 candidates (91.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 4.6b

Counts

80 → 12

regimes713.0ms

Accuracy

18.1% (6.0b remaining)

Error of 11.1b against oracle of 5.0b and baseline of 12.4b

bsearch244.0ms

Steps

Iters	Range		Point
8	7.090339855903539e-72	1.9766524495519856e-68	1.934996812542809e-68
9	-3.0272802816456385e+95	-1.6211672607733614e+87	-1.883004647282782e+89

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	35
1	78	35
2	82	35
3	82	35

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

19242×

body

valid