Details

Time bar (total: 5.3s)

sample52.0ms

Algorithm
intervals
Results
26.0ms286×body80valid
9.0ms107×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize113.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log flip-+
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (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)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify120.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
0236533
1919501
23961487
35001484

prune264.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize113.0ms

Local error

Found 4 expressions with local error:

8.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
6.0ms
(- (- 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)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0225725
1835631
23414609
35001589

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize116.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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 add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
37.0ms
(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)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify187.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (171.0ms)

IterNodesCost
03481856
19131805
241361785
350021704

prune389.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize118.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
4.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.0b
(/ (* a c) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
8×times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out
3×sqrt-prod
2×flip3-- distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 75
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0392629
11966544
25001541

prune281.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.1b

regimes197.0ms

Accuracy

91.2% (1.2b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 20.1b

bsearch150.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
3.6708609126801744e+125
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-2.3202538172935113e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06064
16064

end0.0ms

sample1.3s

Algorithm
intervals
Results
829.0ms8758×body80valid
237.0ms2826×body80nan