Details

Time bar (total: 52.1s)

sample31.0ms

Algorithm
intervals
Results
11.0ms284×body80valid
3.0ms86×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
8.0b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25002510

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
3.0b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (sqrt (- (* z z) (* t a))) z)
33.0ms
(- (* z z) (* t a))
86.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05191327
123801230
250011214

prune365.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
5.4b
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
26.3b
(sqrt (- (* z z) (* t a)))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
445×times-frac
307×add-sqr-sqrt
249×sqrt-prod
222×add-cube-cbrt *-un-lft-identity
98×associate-*r*
33×associate-*l*
31×associate-/r*
30×add-exp-log add-cbrt-cube
20×unswap-sqr
12×cbrt-undiv div-exp
10×div-inv
8×pow1 sqrt-div
6×prod-exp cbrt-unprod
4×associate-/r/ add-log-exp
3×flip3-- flip-- associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 347
Calls
4 calls:
12.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
74.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
87.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
66.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify72.0ms

Algorithm
egg-herbie
Counts
359 → 359
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013125708
150015388

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize28.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (/ (cbrt y) (/ (/ (/ (fabs (cbrt (sqrt (- (* z z) (* t a))))) (cbrt z)) (cbrt z)) (cbrt y))) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
26.3b
(sqrt (- (* z z) (* t a)))
26.3b
(sqrt (- (* z z) (* t a)))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
18968×times-frac
9424×cbrt-prod
8469×add-sqr-sqrt
7733×add-cube-cbrt *-un-lft-identity
4925×associate-*l*
260×div-inv
129×sqrt-prod
124×unswap-sqr
49×add-exp-log
33×associate-*r*
29×add-cbrt-cube
25×cbrt-undiv div-exp
10×sqrt-div prod-exp cbrt-unprod
9×pow1
4×flip3-- flip-- add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 5159
Calls
4 calls:
2.4s
(* (/ (cbrt y) (/ (/ (/ (fabs (cbrt (sqrt (- (* z z) (* t a))))) (cbrt z)) (cbrt z)) (cbrt y))) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
535.0ms
(* (/ (cbrt y) (/ (/ (/ (fabs (cbrt (sqrt (- (* z z) (* t a))))) (cbrt z)) (cbrt z)) (cbrt y))) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
59.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Algorithm
egg-herbie
Counts
5171 → 5171
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05001126020

prune42.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes416.0ms

Accuracy

86.1% (2.7b remaining)

Error of 6.3b against oracle of 3.6b and baseline of 23.1b

bsearch110.0ms

Steps
ItersRangePoint
8
7.491092794297452e+92
6.237674991821684e+96
3.100709508274363e+95
8
-6.141459375605166e+109
-1.770083902157112e+107
-4.611098198946549e+108

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03935
14535
24535

end0.0ms

sample1.0s

Algorithm
intervals
Results
545.0ms8878×body80valid
109.0ms2994×body80nan