Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	189×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	104×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune249.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
9.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`fma-def` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `flip3-+` `fma-neg` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	279	732
1	1153	610
2	5001	597

prune311.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.7b

localize20.0ms

Local error

Found 4 expressions with local error:

11.0b	(+ (- b) (* (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 3.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
8×	`add-log-exp`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 72

Calls

4 calls:

5.0ms	(+ (- b) (* (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (- b) (* (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	351	1045
1	1300	935
2	5001	925

prune395.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b))
0.8b	(- (* b b) (* (* 3.0 a) c))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.6b	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 63

Calls

4 calls:

2.0ms	(cbrt (- b))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
1.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (- b))
48.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
150.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify99.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	248	556
1	816	502
2	3444	487
3	5002	482

prune237.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

regimes345.0ms

Accuracy

83% (3.8b remaining)

Error of 16.4b against oracle of 12.6b and baseline of 35.0b

bsearch114.0ms

Steps

Iters	Range		Point
9	6.122968714791307e-126	2.730466774199498e-117	2.6860323728047766e-117
8	-5.17073721832495e+150	-9.039588443684179e+147	-4.132215651643432e+148

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	37
1	40	37

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	1101×	body	2560	valid
225.0ms	5876×	body	80	valid
160.0ms	883×	body	1280	valid
101.0ms	2996×	body	80	nan
62.0ms	419×	body	640	valid
31.0ms	118×	body	5120	valid
24.0ms	235×	body	320	valid
9.0ms	125×	body	160	valid