Details

Time bar (total: 6.1s)

sample47.0ms

Algorithm
intervals
Results
31.0ms445×body80valid

simplify112.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 143
Calls
4 calls:
8.0ms
(* (* (fabs x) (fabs x)) (fabs x))
326.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
30.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series413.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (fabs x) (fabs x)) (fabs x))
337.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify54.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010064086
150013203

prune636.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs x) (fabs x)) (fabs x))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (pow (fabs x) 3) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0b
(sqrt PI)

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 143
Calls
4 calls:
8.0ms
(* (* (fabs x) (fabs x)) (fabs x))
27.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
223.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (pow (fabs x) 3) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0ms
(sqrt PI)

series415.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
45.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
339.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (pow (fabs x) 3) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.0ms
(sqrt PI)

simplify52.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010113873
150012962

prune689.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify48.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
092312
1290300
21422292
35002292

prune352.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.3b
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (fma (/ 1.0 21.0) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (sqrt 1.0)) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
105×sqrt-prod
97×add-sqr-sqrt
82×times-frac
70×associate-*l*
57×add-cube-cbrt *-un-lft-identity
38×add-exp-log
30×add-cbrt-cube
26×associate-*r*
15×unswap-sqr
14×prod-exp
10×div-exp cbrt-unprod
8×pow1 cbrt-undiv
5×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-exp *-commutative
1×cube-mult frac-times unpow3 pow-prod-down associate-*l/
Counts
4 → 186
Calls
4 calls:
12.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
46.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (fma (/ 1.0 21.0) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (sqrt 1.0)) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series412.0ms

Counts
4 → 8
Calls
4 calls:
50.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
362.0ms
(* (/ (sqrt 1.0) (sqrt (sqrt PI))) (/ (* (fma (/ 1.0 21.0) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) (sqrt 1.0)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify129.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07305098
138564520
250024299

prune833.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04739
14739

end0.0ms

sample1.0s

Algorithm
intervals
Results
881.0ms13960×body80valid