Details

Time bar (total: 6.7s)

sample68.0ms

Algorithm
intervals
Results
14.0ms507×pre80true
13.0ms145×body160valid
12.0ms251×body80nan
8.0ms58×body320valid
3.0ms53×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 43.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438854
11702750
25002735

prune251.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New966102
Fresh000
Picked101
Done000
Total976103

Merged error: 0.2b

Counts
103 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify164.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
08325099
139673830
250013828

prune539.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2358243
Fresh415
Picked011
Done000
Total23910249

Merged error: 0b

Counts
249 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
0.3b
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
0.4b
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
37.7b
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log add-cbrt-cube
42×sqrt-div
41×prod-exp cbrt-unprod
25×cbrt-undiv associate-*r/ div-exp
23×flip3-- flip--
22×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
16×frac-add
13×associate-*r*
12×times-frac
9×frac-times
8×pow1
7×associate-*l*
6×unpow-prod-down cube-prod sqrt-prod add-log-exp
5×associate-*l/
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×pow-unpow pow-pow div-inv
2×distribute-lft-neg-out cube-div unswap-sqr
1×+-commutative cube-mult pow-to-exp distribute-rgt-out fma-def frac-2neg sqrt-pow1 flip3-+ pow1/2 unpow3 unsub-neg pow-prod-down pow-exp clear-num associate-/r* sum-log *-commutative sqrt-pow2 flip-+ associate-/l* rem-cube-cbrt sqr-pow
Counts
4 → 162
Calls
4 calls:
5.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
52.0ms
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
32.0ms
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
13.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series908.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
387.0ms
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
350.0ms
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
119.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011995749
150024124

prune580.0ms

Filtered
174 candidates to 107 candidates (61.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1740174
Fresh088
Picked011
Done011
Total17410184

Merged error: 0b

Counts
184 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
0.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
0.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-- pow1/3 flip--
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
11.0ms
(* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

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

simplify145.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02731280
110231201
248481129
350011129

prune364.0ms

Filtered
107 candidates to 83 candidates (77.6%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1070107
Fresh077
Picked011
Done022
Total10710117

Merged error: 0b

Counts
117 → 10

regimes141.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12713
22713

end0.0ms

sample1.9s

Algorithm
intervals
Results
457.0ms4841×body160valid
449.0ms16380×pre80true
389.0ms8380×body80nan
184.0ms1337×body320valid
90.0ms1822×body80valid