Details

sample74.0ms

Algorithm

intervals

Results

39.0ms

597×

body

valid

simplify88.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c z) (* i a))
5.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.1b	(* b (- (* c z) (* i a)))
6.6b	(* x (- (* y z) (* t a)))

rewrite25.0ms

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

series722.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c z) (* i a))
551.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
63.0ms	(* b (- (* c z) (* i a)))
68.0ms	(* x (- (* y z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	373	645
1	1485	568
2	5001	568

prune423.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* z c) (* a i))) (* b (fma (- a) i (* a i))))))
6.1b	(* b (- (* z c) (* a i)))
6.6b	(* x (- (* y z) (* t a)))
50.7b	(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:

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

series3.6s

Counts

4 → 12

Calls

4 calls:

3.4s	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* z c) (* a i))) (* b (fma (- a) i (* a i))))))
70.0ms	(* b (- (* z c) (* a i)))
67.0ms	(* x (- (* y z) (* t a)))
25.0ms	(fma (- a) i (* a i))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	365	664
1	1456	577
2	5001	577

prune459.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize30.0ms

Local error

Found 4 expressions with local error:

6.1b	(* b (- (* z c) (* a i)))
6.6b	(* x (fma y z (- (* a t))))
50.7b	(fma (- a) i (* a i))
52.1b	(fma (- a) t (* a t))

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×	`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:

10.0ms	(* b (- (* z c) (* a i)))
3.0ms	(* x (fma y z (- (* a t))))
0.0ms	(fma (- a) i (* a i))
0.0ms	(fma (- a) t (* a t))

series197.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* b (- (* z c) (* a i)))
72.0ms	(* x (fma y z (- (* a t))))
26.0ms	(fma (- a) i (* a i))
31.0ms	(fma (- a) t (* a t))

simplify119.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	280	428
1	1108	373
2	4522	373
3	5001	373

prune473.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize35.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (- (* y z) (* t a)))
7.8b	(cbrt (- (* y z) (* t a)))
7.8b	(cbrt (- (* y z) (* t a)))
50.7b	(fma (- a) i (* a i))

rewrite8.0ms

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:

2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))
0.0ms	(fma (- a) i (* a i))

series389.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (- (* y z) (* t a)))
126.0ms	(cbrt (- (* y z) (* t a)))
118.0ms	(cbrt (- (* y z) (* t a)))
27.0ms	(fma (- a) i (* a i))

simplify139.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	208	512
1	583	478
2	1829	460
3	4900	452
4	5001	452

prune467.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

regimes633.0ms

Accuracy

-21.7% (9.1b remaining)

Error of 14.3b against oracle of 5.3b and baseline of 12.7b

bsearch216.0ms

Steps

Iters	Range		Point
7	2.9573163455465304e+172	3.559110388059871e+174	3.505890669512003e+174
7	-5.122380833550238e+149	-1.0561577110665917e+148	-3.130219245178589e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	36
1	60	36

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s

18839×

body

valid