Details

sample155.0ms

Algorithm

intervals

Results

118.0ms

632×

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c t) (* i y))
3.6b	(* b (- (* c z) (* i a)))
3.8b	(* x (- (* y z) (* t a)))
4.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

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

series731.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c t) (* i y))
61.0ms	(* b (- (* c z) (* i a)))
69.0ms	(* x (- (* y z) (* t a)))
561.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

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

prune435.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b	(* b (- (* c z) (* i a)))
3.8b	(* x (- (* y z) (* t a)))
4.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
49.0b	(fma (- a) i (* a i))

rewrite22.0ms

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

series3.7s

Counts

4 → 12

Calls

4 calls:

64.0ms	(* b (- (* c z) (* i a)))
67.0ms	(* x (- (* y z) (* t 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))))))
29.0ms	(fma (- a) i (* a i))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	360	664
1	1457	577
2	5001	577

prune466.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b	(* b (- (* c z) (* i a)))
3.8b	(* x (- (* y z) (* t a)))
4.9b	(* (- (* c t) (* i y)) j)
49.0b	(fma (- a) i (* a i))

rewrite32.0ms

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(* b (- (* c z) (* i a)))
10.0ms	(* x (- (* y z) (* t a)))
9.0ms	(* (- (* c t) (* i y)) j)
0.0ms	(fma (- a) i (* a i))

series258.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* b (- (* c z) (* i a)))
79.0ms	(* x (- (* y z) (* t a)))
66.0ms	(* (- (* c t) (* i y)) j)
33.0ms	(fma (- a) i (* a i))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	434	566
1	1738	496
2	5002	496

prune668.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (cbrt x) (- (* y z) (* t a)))
3.6b	(* b (- (* c z) (* i a)))
4.9b	(* (- (* c t) (* i y)) j)
49.0b	(fma (- a) i (* a i))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (cbrt x) (- (* y z) (* t a)))
10.0ms	(* b (- (* c z) (* i a)))
10.0ms	(* (- (* c t) (* i y)) j)
0.0ms	(fma (- a) i (* a i))

series463.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (cbrt x) (- (* y z) (* t a)))
74.0ms	(* b (- (* c z) (* i a)))
69.0ms	(* (- (* c t) (* i y)) j)
31.0ms	(fma (- a) i (* a i))

simplify62.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	470	638
1	1892	573
2	5002	573

prune547.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.7b

regimes979.0ms

Accuracy

3% (7.6b remaining)

Error of 12.1b against oracle of 4.5b and baseline of 12.3b

bsearch220.0ms

Steps

Iters	Range		Point
6	1.9967792972069281e-218	2.961033549038271e-217	1.482328301763721e-217
7	-4.6580600805654477e-156	-2.5744595640146742e-157	-2.8874577549273917e-157

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	39
1	60	39
2	71	39
3	71	39

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.7s

19135×

body

valid