Details

Time bar (total: 52.3s)

sample31.0ms

Algorithm
intervals
Results
13.0ms284×body80valid
3.0ms86×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune2.0ms

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)))

rewrite28.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368631
11935560
25002551

prune265.0ms

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)))

rewrite31.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
8.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
5.0ms
(sqrt (- (* z z) (* t a)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (sqrt (- (* z z) (* t a))) z)
32.0ms
(- (* z z) (* t a))
81.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05431379
124481281
250011260

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

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)))

rewrite151.0ms

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×expm1-log1p-u associate-/r/ log1p-expm1-u 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 → 355
Calls
4 calls:
12.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
100.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
7.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z))
83.0ms
(* (/ x (sqrt (sqrt (- (* z z) (* t a))))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) z)))
62.0ms
(sqrt (- (* z z) (* t a)))
58.0ms
(sqrt (- (* z z) (* t a)))

simplify82.0ms

Algorithm
egg-herbie
Counts
367 → 367
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013265774
150025454

prune922.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize29.0ms

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)))

rewrite4.0s

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×expm1-log1p-u flip3-- flip-- log1p-expm1-u 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 → 5167
Calls
4 calls:
3.1s
(* (/ (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)))
5.0ms
(sqrt (- (* z z) (* t a)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
483.0ms
(* (/ (cbrt y) (/ (/ (/ (fabs (cbrt (sqrt (- (* z z) (* t a))))) (cbrt z)) (cbrt z)) (cbrt y))) (/ x (sqrt (sqrt (- (* z z) (* t a))))))
60.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Algorithm
egg-herbie
Counts
5179 → 5179
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05002126094

prune42.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes404.0ms

Accuracy

86.1% (2.7b remaining)

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

bsearch113.0ms

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

sample789.0ms

Algorithm
intervals
Results
344.0ms8878×body80valid
103.0ms2994×body80nan