Details

Time bar (total: 6.0s)

sample56.0ms

Algorithm
intervals
Results
30.0ms286×body80valid
9.0ms107×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize118.0ms

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)))

rewrite25.0ms

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

series270.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify150.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0264600
11046558
24657542
35001542

prune374.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize126.0ms

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)))

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:
84.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify180.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune466.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize125.0ms

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)))

rewrite52.0ms

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:
40.0ms
(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)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify185.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03621930
19701879
244771859
350011859

prune495.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize126.0ms

Local error

Found 4 expressions with local error:

6.0b
(/ (* a c) b)
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)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×flip3-- times-frac associate-/r* flip--
2×cbrt-undiv neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-exp
1×associate--l- neg-sub0 sub-neg frac-2neg neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l* difference-of-squares
Counts
4 → 94
Calls
4 calls:
3.0ms
(/ (* a c) b)
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)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* a c) b)
81.0ms
(- (- 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)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03771335
115891055
250011034

prune450.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.1b

regimes223.0ms

Accuracy

91.2% (1.2b remaining)

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

bsearch158.0ms

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
06472
16472

end0.0ms

sample1.3s

Algorithm
intervals
Results
836.0ms8758×body80valid
234.0ms2826×body80nan