Details

sample74.0ms

Algorithm

intervals

Results

38.0ms

608×

body

valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
2.9b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.0b	(* x (- (* y z) (* t a)))
5.4b	(* b (- (* c z) (* t i)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

10.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* t i)))

series1.0s

Counts

4 → 12

Calls

4 calls:

253.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
604.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
77.0ms	(* x (- (* y z) (* t a)))
80.0ms	(* b (- (* c z) (* t i)))

simplify96.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	578	1034
1	2633	947
2	5003	943

prune563.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b	(fma (- (* c a) (* y i)) j (- (- (* x (- (* y z) (* t a))) (* (fma c z (- (* i t))) b)) (* (fma (- i) t (* i t)) b)))
5.0b	(* x (- (* y z) (* t a)))
5.4b	(* (fma c z (- (* i t))) b)
49.2b	(fma (- i) t (* i t))

rewrite13.0ms

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

Counts

4 → 68

Calls

4 calls:

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

series3.8s

Counts

4 → 12

Calls

4 calls:

3.7s	(fma (- (* c a) (* y i)) j (- (- (* x (- (* y z) (* t a))) (* (fma c z (- (* i t))) b)) (* (fma (- i) t (* i t)) b)))
72.0ms	(* x (- (* y z) (* t a)))
77.0ms	(* (fma c z (- (* i t))) b)
27.0ms	(fma (- i) t (* i t))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	304	614
1	1101	529
2	5002	529

prune497.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.1b

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (fma c z (- (* i t))))
7.1b	(cbrt (fma c z (- (* i t))))
7.1b	(cbrt (fma c z (- (* i t))))
49.2b	(fma (- i) t (* i t))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (fma c z (- (* i t))))
1.0ms	(cbrt (fma c z (- (* i t))))
1.0ms	(cbrt (fma c z (- (* i t))))
1.0ms	(fma (- i) t (* i t))

series447.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (fma c z (- (* i t))))
140.0ms	(cbrt (fma c z (- (* i t))))
144.0ms	(cbrt (fma c z (- (* i t))))
26.0ms	(fma (- i) t (* i t))

simplify119.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (113.0ms)

Iter	Nodes	Cost
0	142	422
1	327	388
2	999	370
3	3290	359
4	5001	350

prune514.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.1b

localize36.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (- (* y z) (* t a)))
6.9b	(cbrt (- (* y z) (* t a)))
6.9b	(cbrt (- (* y z) (* t a)))
49.2b	(fma (- i) t (* i t))

rewrite13.0ms

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:

4.0ms	(cbrt (- (* y z) (* t a)))
4.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
1.0ms	(fma (- i) t (* i t))

series427.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (- (* y z) (* t a)))
136.0ms	(cbrt (- (* y z) (* t a)))
133.0ms	(cbrt (- (* y z) (* t a)))
26.0ms	(fma (- i) t (* i t))

simplify150.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	208	512
1	583	478
2	1826	460
3	4900	452
4	5001	452

prune495.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 3.1b

regimes1.3s

Accuracy

5.6% (7.1b remaining)

Error of 12.0b against oracle of 4.8b and baseline of 12.4b

bsearch317.0ms

Steps

Iters	Range		Point
11	4.0465437293808955e+170	1.8775310523978808e+191	2.8850197795509696e+190
10	-4.835776492790962e+111	-3.851975220168129e+98	-4.4644369022584814e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	36
1	63	36
2	63	36

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

18981×

body

valid