Details

sample43.0ms

Algorithm

intervals

Results

8.0ms	36×	body	1280	valid
8.0ms	40×	body	2560	valid
6.0ms	181×	body	80	valid
3.0ms	99×	body	80	nan
3.0ms	21×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b	(- (* b b) (* (* 3.0 a) c))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

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)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

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

prune250.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.4b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
0.6b	(- (* b b) (* 3.0 (* a c)))
23.8b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

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-l` `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-r` `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))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
42.0ms	(- (* b b) (* 3.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	330	529
1	1217	478
2	5001	467

prune294.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
0.6b	(- (* b b) (* (* 3.0 a) c))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

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

series225.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
43.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune280.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
12.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

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))
5.0ms	(+ (- 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)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(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

prune277.0ms

Filtered

87 candidates to 73 candidates (83.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.3b

regimes287.0ms

Accuracy

86.4% (3.0b remaining)

Error of 15.5b against oracle of 12.5b and baseline of 34.8b

bsearch95.0ms

Steps

Iters	Range		Point
8	3.4933217786584286e-62	2.5836749552794725e-58	2.9472649968823877e-60
8	-6.693693221964152e+155	-2.9183492048471296e+152	-1.3396975574702294e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

241.0ms	1141×	body	2560	valid
207.0ms	5762×	body	80	valid
166.0ms	939×	body	1280	valid
105.0ms	2987×	body	80	nan
62.0ms	466×	body	640	valid
26.0ms	230×	body	320	valid
23.0ms	90×	body	5120	valid
7.0ms	109×	body	160	valid