Details

sample73.0ms

Algorithm

intervals

Results

38.0ms

595×

body

valid

simplify92.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c z) (* i a))
4.7b	(* j (- (* c t) (* i y)))
5.5b	(* b (- (* c z) (* i a)))
5.9b	(* x (- (* y z) (* t a)))

rewrite37.0ms

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:

3.0ms	(- (* c z) (* i a))
12.0ms	(* j (- (* c t) (* i y)))
10.0ms	(* b (- (* c z) (* i a)))
10.0ms	(* x (- (* y z) (* t a)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* c z) (* i a))
76.0ms	(* j (- (* c t) (* i y)))
77.0ms	(* b (- (* c z) (* i a)))
72.0ms	(* x (- (* y z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

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

prune535.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.0b

localize25.0ms

Local error

Found 4 expressions with local error:

4.7b	(* j (- (* c t) (* i y)))
5.5b	(* b (- (* z c) (* a i)))
5.9b	(* x (- (* y z) (* t a)))
50.9b	(fma (- a) i (* a i))

rewrite34.0ms

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:

12.0ms	(* j (- (* c t) (* i y)))
10.0ms	(* b (- (* z c) (* a i)))
10.0ms	(* x (- (* y z) (* t a)))
0.0ms	(fma (- a) i (* a i))

series256.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* j (- (* c t) (* i y)))
77.0ms	(* b (- (* z c) (* a i)))
74.0ms	(* x (- (* y z) (* t a)))
29.0ms	(fma (- a) i (* a i))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	461	602
1	1904	532
2	5001	532

prune563.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.0b

localize30.0ms

Local error

Found 4 expressions with local error:

5.5b	(* b (- (* z c) (* a i)))
5.9b	(* x (- (* y z) (* t a)))
50.9b	(fma (- a) i (* a i))
51.1b	(fma (- y) i (* y i))

rewrite24.0ms

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:

10.0ms	(* b (- (* z c) (* a i)))
12.0ms	(* x (- (* y z) (* t a)))
0.0ms	(fma (- a) i (* a i))
0.0ms	(fma (- y) i (* y i))

series209.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* b (- (* z c) (* a i)))
74.0ms	(* x (- (* y z) (* t a)))
28.0ms	(fma (- a) i (* a i))
26.0ms	(fma (- y) i (* y i))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	468
1	1342	412
2	5001	412

prune562.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize35.0ms

Local error

Found 4 expressions with local error:

5.9b	(* x (fma y z (- (* a t))))
50.1b	(fma (- a) t (* a t))
50.9b	(fma (- a) i (* a i))
51.1b	(fma (- y) i (* y i))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`fma-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

4.0ms	(* x (fma y z (- (* a t))))
0.0ms	(fma (- a) t (* a t))
0.0ms	(fma (- a) i (* a i))
0.0ms	(fma (- y) i (* y i))

series169.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (fma y z (- (* a t))))
28.0ms	(fma (- a) t (* a t))
32.0ms	(fma (- a) i (* a i))
27.0ms	(fma (- y) i (* y i))

simplify58.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	150	294
1	521	253
2	2138	253
3	5001	229

prune406.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

regimes1.1s

Accuracy

3.9% (3.7b remaining)

Error of 12.3b against oracle of 8.6b and baseline of 12.5b

bsearch253.0ms

Steps

Iters	Range		Point
8	1.531449904657733e-235	9.81316078903804e-233	1.5869106614607107e-234
10	-3.8730876141943625e-165	-6.332287579989247e-178	-3.0773273627394588e-176

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	39
1	88	39
2	88	39

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19232×

body

valid