Details

sample71.0ms

Algorithm

intervals

Results

36.0ms

577×

body

valid

simplify91.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* c z) (* i a))
4.7b	(* j (- (* c t) (* i y)))
4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (- (* y z) (* t a)))

rewrite26.0ms

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

Counts

4 → 100

Calls

4 calls:

4.0ms	(- (* c z) (* i a))
7.0ms	(* j (- (* c t) (* i y)))
6.0ms	(* b (- (* c z) (* i a)))
7.0ms	(* x (- (* y z) (* t a)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* c z) (* i a))
65.0ms	(* j (- (* c t) (* i y)))
71.0ms	(* b (- (* c z) (* i a)))
71.0ms	(* x (- (* y z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	478	643
1	1976	572
2	5001	572

prune578.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.1b

localize25.0ms

Local error

Found 4 expressions with local error:

4.7b	(* j (- (* c t) (* i y)))
4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (fma y z (- (* a t))))
48.6b	(fma (- a) t (* a t))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* j (- (* c t) (* i y)))
79.0ms	(* b (- (* c z) (* i a)))
78.0ms	(* x (fma y z (- (* a t))))
26.0ms	(fma (- a) t (* a t))

simplify53.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	412	562
1	1685	493
2	5001	493

prune799.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.1b

localize34.0ms

Local error

Found 4 expressions with local error:

4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (fma y z (- (* a t))))
48.6b	(fma (- a) t (* a t))
50.2b	(fma (- y) i (* y i))

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

series211.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* b (- (* c z) (* i a)))
78.0ms	(* x (fma y z (- (* a t))))
34.0ms	(fma (- a) t (* a t))
26.0ms	(fma (- y) i (* y i))

simplify122.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	285	428
1	1111	373
2	4531	373
3	5001	373

prune583.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.1b

localize38.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (* x (fma y z (- (* a t)))))
5.7b	(cbrt (* x (fma y z (- (* a t)))))
48.6b	(fma (- a) t (* a t))
50.2b	(fma (- y) i (* y i))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

2.0ms	(cbrt (* x (fma y z (- (* a t)))))
2.0ms	(cbrt (* x (fma y z (- (* a t)))))
1.0ms	(fma (- a) t (* a t))
1.0ms	(fma (- y) i (* y i))

series374.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (* x (fma y z (- (* a t)))))
156.0ms	(cbrt (* x (fma y z (- (* a t)))))
32.0ms	(fma (- a) t (* a t))
28.0ms	(fma (- y) i (* y i))

simplify48.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	153	316
1	393	280
2	1416	274
3	5002	252

prune415.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 7.1b

regimes1.5s

Accuracy

-10.4% (4.6b remaining)

Error of 12.7b against oracle of 8.1b and baseline of 12.3b

bsearch189.0ms

Steps

Iters	Range		Point
4	3.252789471393584e-124	5.021907344406643e-124	3.288698165822717e-124
10	-2.5799640052418466e-113	-3.3117496423123305e-126	-3.373588334677838e-126

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	75
1	91	75
2	91	75

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

18962×

body

valid