Details

sample78.0ms

Algorithm

intervals

Results

42.0ms

634×

body

valid

simplify97.0ms

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: 10.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y z) (* t a))
3.9b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.0b	(* x (- (* y z) (* t a)))
5.6b	(* b (- (* c z) (* t i)))

rewrite26.0ms

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

series744.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* y z) (* t a))
565.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
65.0ms	(* x (- (* y z) (* t a)))
69.0ms	(* b (- (* c z) (* t i)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	645
1	1500	568
2	5001	568

prune459.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* y z) (* t a))
4.0b	(* x (- (* y z) (* t a)))
4.7b	(* j (- (* c a) (* y i)))
5.6b	(* b (- (* c z) (* t i)))

rewrite36.0ms

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

series245.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* y z) (* t a))
71.0ms	(* x (- (* y z) (* t a)))
68.0ms	(* j (- (* c a) (* y i)))
70.0ms	(* b (- (* c z) (* t i)))

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	476	643
1	1969	572
2	5002	572

prune503.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

4.0b	(* x (fma y z (- (* a t))))
4.7b	(* j (- (* c a) (* y i)))
5.6b	(* b (- (* c z) (* t i)))
49.8b	(fma (- a) t (* a t))

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×	`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:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* x (fma y z (- (* a t))))
69.0ms	(* j (- (* c a) (* y i)))
67.0ms	(* b (- (* c z) (* t i)))
30.0ms	(fma (- a) t (* a t))

simplify53.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	410	562
1	1678	493
2	5001	493

prune515.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.2b

localize25.0ms

Local error

Found 4 expressions with local error:

5.6b	(* b (- (* c z) (* t i)))
6.0b	(cbrt (- (* y z) (* t a)))
6.0b	(cbrt (- (* y z) (* t a)))
6.0b	(cbrt (- (* y z) (* t a)))

rewrite19.0ms

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:

10.0ms	(* b (- (* c z) (* t i)))
2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* b (- (* c z) (* t i)))
119.0ms	(cbrt (- (* y z) (* t a)))
125.0ms	(cbrt (- (* y z) (* t a)))
119.0ms	(cbrt (- (* y z) (* t a)))

simplify113.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	335	646
1	1158	598
2	4180	580
3	5001	580

prune463.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 3.2b

regimes990.0ms

Accuracy

-11.9% (8.7b remaining)

Error of 13.2b against oracle of 4.5b and baseline of 12.3b

bsearch200.0ms

Steps

Iters	Range		Point
6	-1.2122084782473737e+51	-2.000773547965604e+50	-1.1972985037498114e+51
9	-4.123571834400257e+110	-2.7563809427078637e+104	-2.785006001953297e+104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	26
1	63	26
2	63	26

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19263×

body

valid