Details

Time bar (total: 4.6s)

sample44.0ms

Algorithm
intervals
Results
21.0ms285×body80valid
5.0ms79×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
4.5b
(* (* x y) z)
7.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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))
9.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0368630
11941560
25001551

prune271.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
3.0b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
9.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
35.0ms
(- (* z z) (* t a))
81.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04531067
12239963
25001942

prune332.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
23×prod-exp cbrt-unprod
18×sqrt-div
13×associate-*r*
12×pow1 cbrt-div
11×add-sqr-sqrt
9×flip3-- sqrt-prod flip--
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp associate-/r/
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
2×associate-*l/
1×times-frac associate-*l* *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
46.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
5.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
59.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05151386
126241113
250011011

prune394.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.7b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.8b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
18.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
21.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
51.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
79.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0425829
11848729
25001717

prune253.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.1b

regimes407.0ms

Accuracy

86.2% (2.6b remaining)

Error of 6.0b against oracle of 3.4b and baseline of 22.4b

bsearch109.0ms

Steps
ItersRangePoint
10
1.0894270704813426e+95
1.5741303840168087e+105
6.7193907563449e+103
7
-1.5931363873182533e+155
-1.016503209116054e+153
-8.778173507641342e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13828
23828

end0.0ms

sample1.3s

Algorithm
intervals
Results
665.0ms8879×body80valid
207.0ms2979×body80nan