Details

Time bar (total: 5.7s)

sample49.0ms

Algorithm
intervals
Results
32.0ms616×body80valid

simplify80.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (+ 3.0 a))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ fma-udef
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
15.0ms
(* (* b b) (+ 3.0 a))

series299.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
50.0ms
(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
35.0ms
(* (* b b) (+ 3.0 a))

simplify46.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0335551
11554479
25001471

prune262.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (+ 3.0 a))
11.6b
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp cbrt-unprod sqr-pow
2×cube-mult pow-to-exp pow-pow unpow3 associate-*r/ pow-exp
1×distribute-rgt-in distribute-lft-in flip3-+ pow1/3 associate-*l* *-commutative rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 93
Calls
4 calls:
1.0ms
(pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
15.0ms
(* (* b b) (+ 3.0 a))
2.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

series907.0ms

Counts
4 → 12
Calls
4 calls:
655.0ms
(pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
106.0ms
(pow (+ (* a a) (* b b)) 2.0)
39.0ms
(* (* b b) (+ 3.0 a))
106.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

simplify250.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04321233
120591126
250021113

prune309.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

11.6b
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) 1.0)) 3))
18.7b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.7b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.7b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
3×cube-prod
1×cube-mult unpow3 rem-cbrt-cube
Counts
4 → 74
Calls
4 calls:
1.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) 1.0)) 3))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series542.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) 1.0)) 3))
145.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify101.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
02271473
18191406
229101380
350021368

prune385.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (+ 3.0 a))
1.8b
(expm1 (log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))))
3.8b
(log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)))
11.6b
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×*-un-lft-identity
9×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
5×expm1-log1p-u
4×associate-*r* log1p-expm1-u add-log-exp
3×unpow-prod-down cube-prod pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in cube-mult log1p-udef expm1-log1p distribute-lft-in flip3-+ pow1/3 unpow3 log1p-expm1 associate-*l* *-commutative rem-cbrt-cube flip-+ distribute-lft-out expm1-udef unswap-sqr sqr-pow
Counts
4 → 71
Calls
4 calls:
18.0ms
(* (* b b) (+ 3.0 a))
0.0ms
(expm1 (log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))))
0.0ms
(log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)))
2.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

series411.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
146.0ms
(expm1 (log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))))
129.0ms
(log1p (cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)))
102.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

simplify54.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04371069
118941007
25001997

prune275.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01912
11912

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20541×body80valid