Details

Time bar (total: 4.3s)

sample30.0ms

Algorithm
intervals
Results
14.0ms138×pre10240exit
4.0ms256×body80valid
2.0ms118×pre80true

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1123
2123

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b
(/ x0 (- 1.0 x1))
7.7b
(- (/ x0 (- 1.0 x1)) x0)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
16×times-frac
12×add-cube-cbrt
6×difference-of-squares
5×associate-/r* distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
5.0ms
(/ x0 (- 1.0 x1))
30.0ms
(- (/ x0 (- 1.0 x1)) x0)

series79.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ x0 (- 1.0 x1))
46.0ms
(- (/ x0 (- 1.0 x1)) x0)

simplify92.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0244328
1801315
23123310
35001310

prune85.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ x0 (- 1.0 x1))
0.7b
(/ x0 (- 1.0 x1))
0.7b
(/ x0 (- 1.0 x1))
6.4b
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
45×times-frac
34×add-cube-cbrt
15×associate-/r*
13×difference-of-squares
12×distribute-lft-out--
10×add-exp-log add-cbrt-cube
9×associate-/l*
6×associate-/r/ add-log-exp
4×pow1 flip3-- flip--
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×sub-neg diff-log
Counts
4 → 124
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
10.0ms
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

series175.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ x0 (- 1.0 x1))
37.0ms
(/ x0 (- 1.0 x1))
33.0ms
(/ x0 (- 1.0 x1))
72.0ms
(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify155.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0288828
11116773
24811759
35001759

prune238.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
0.7b
(/ x0 (- 1.0 x1))
0.7b
(/ x0 (- 1.0 x1))
6.4b
(- (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
108×times-frac
86×*-un-lft-identity
56×add-cube-cbrt
54×associate-*r*
46×sqrt-prod
30×cbrt-prod
29×add-exp-log
22×add-cbrt-cube
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-*l*
10×associate-/r*
9×cbrt-undiv div-exp
8×prod-exp associate-/r/ cbrt-unprod
6×pow1 associate-/l* add-log-exp
5×flip3-- flip--
4×sqrt-div div-inv
2×frac-2neg clear-num
1×frac-times sub-neg diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 193
Calls
4 calls:
54.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
7.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
90.0ms
(- (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

series209.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
33.0ms
(/ x0 (- 1.0 x1))
33.0ms
(/ x0 (- 1.0 x1))
91.0ms
(- (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify105.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
08222365
143022173
250021936

prune443.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
0.9b
(pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3)
1.0b
(pow (* x0 x0) 3)
5.8b
(- (pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3) (pow (* x0 x0) 3))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
94×add-exp-log
78×times-frac
73×add-cbrt-cube
54×*-un-lft-identity associate-*r*
46×sqrt-prod
39×prod-exp cbrt-unprod
38×add-cube-cbrt
30×cbrt-prod
28×cbrt-undiv div-exp
20×pow1
17×pow-exp rem-cube-cbrt
15×difference-of-squares unswap-sqr
14×associate-*l*
9×pow-pow
8×distribute-lft-out-- sqr-pow
7×cube-div
6×frac-times pow-unpow associate-*l/ add-log-exp
5×pow-prod-down
4×unpow-prod-down sqrt-div cube-prod associate-*r/ associate-/r/
3×flip3-- flip--
2×cube-mult pow-to-exp unpow3 div-inv
1×difference-cubes pow2 sub-neg pow-plus diff-log pow-sqr *-commutative pow-prod-up
Counts
4 → 211
Calls
4 calls:
57.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
90.0ms
(pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3)
3.0ms
(pow (* x0 x0) 3)
11.0ms
(- (pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3) (pow (* x0 x0) 3))

series350.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1))))
100.0ms
(pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3)
42.0ms
(pow (* x0 x0) 3)
161.0ms
(- (pow (* (* (/ (* (cbrt x0) (cbrt x0)) (sqrt (- 1.0 x1))) (/ (cbrt x0) (sqrt (- 1.0 x1)))) (/ x0 (- 1.0 x1))) 3) (pow (* x0 x0) 3))

simplify57.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011003000
150012779

prune958.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.6b

regimes94.0ms

Accuracy

78.4% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 6.2b

bsearch1.0ms

Steps
ItersRangePoint
0
0.9814
0.999791
0.9905955

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049166
149166

end0.0ms

sample730.0ms

Algorithm
intervals
Results
383.0ms3984×pre10240exit
142.0ms8000×body80valid
66.0ms4016×pre80true