Details

sample67.0ms

Algorithm

intervals

Results

40.0ms	280×	body	80	valid
11.0ms	100×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize120.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	264	602
1	1046	558
2	4657	542
3	5001	542

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize120.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	170	542
1	665	506
2	2968	498
3	5001	488

prune352.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.1b

localize119.0ms

Local error

Found 4 expressions with local error:

9.7b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

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

series302.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify182.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	283	1391
1	998	1121
2	4723	1013
3	5001	1013

prune455.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.0b

localize126.0ms

Local error

Found 4 expressions with local error:

24.2b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
25.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

33.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify194.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	362	1936
1	979	1879
2	4487	1859
3	5001	1859

prune595.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.0b

regimes178.0ms

Accuracy

94.3% (0.7b remaining)

Error of 8.3b against oracle of 7.6b and baseline of 20.1b

bsearch178.0ms

Steps

Iters	Range		Point
7	6.714891876596302e+121	1.686395921989292e+123	1.4702486099407425e+123
8	-5.9769678902734345e+158	-1.9689745148643392e+154	-2.0079720992890853e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	54
1	50	54

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8741×	body	80	valid
338.0ms	2931×	body	80	nan