Details

sample75.0ms

Algorithm

intervals

Results

40.0ms

600×

body

valid

simplify98.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c t) (* i y))
3.9b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
4.9b	(* x (- (* y z) (* t a)))
7.1b	(* b (- (* c z) (* i a)))

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 t) (* i y))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
7.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* i a)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* c t) (* i y))
588.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
71.0ms	(* x (- (* y z) (* t a)))
72.0ms	(* b (- (* c z) (* i a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

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

prune477.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c z) (* i a))
3.9b	(fma (fma c t (- (* i y))) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
4.9b	(* x (- (* y z) (* t a)))
7.1b	(* b (- (* c z) (* i a)))

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

series780.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* c z) (* i a))
598.0ms	(fma (fma c t (- (* i y))) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
72.0ms	(* x (- (* y z) (* t a)))
71.0ms	(* b (- (* c z) (* i a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	374	645
1	1484	568
2	5001	568

prune498.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.0b

localize33.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma (fma c t (- (* i y))) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
4.9b	(* x (fma y z (- (* a t))))
7.1b	(* b (- (* c z) (* i a)))
52.9b	(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:

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

series3.6s

Counts

4 → 12

Calls

4 calls:

3.4s	(fma (fma c t (- (* i y))) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
80.0ms	(* x (fma y z (- (* a t))))
75.0ms	(* b (- (* c z) (* i a)))
27.0ms	(fma (- a) t (* a t))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	316	624
1	1246	538
2	5001	538

prune495.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.0b

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (- (* c t) (* i y)))
5.5b	(cbrt (- (* c t) (* i y)))
5.5b	(cbrt (- (* c t) (* i y)))
7.1b	(* b (- (* c z) (* i a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

4.0ms	(cbrt (- (* c t) (* i y)))
4.0ms	(cbrt (- (* c t) (* i y)))
4.0ms	(cbrt (- (* c t) (* i y)))
7.0ms	(* b (- (* c z) (* i a)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (- (* c t) (* i y)))
348.0ms	(cbrt (- (* c t) (* i y)))
128.0ms	(cbrt (- (* c t) (* i y)))
74.0ms	(* b (- (* c z) (* i a)))

simplify110.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	337	646
1	1155	598
2	4177	580
3	5001	580

prune469.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.0b

regimes1.1s

Accuracy

-0.5% (7.9b remaining)

Error of 12.2b against oracle of 4.3b and baseline of 12.1b

bsearch225.0ms

Steps

Iters	Range		Point
7	7.688693475640985e+130	3.7304168740988947e+132	3.668522594214648e+132
9	-2.4016934733075356e+92	-3.4462837374364854e+87	-2.3811833313536233e+92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	32
1	65	32
2	65	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19172×

body

valid