Details

Time bar (total: 2.4m)

sample32.0ms

Algorithm
intervals
Results
13.0ms293×body80valid
3.0ms100×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.2b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.0b
(* (* x y) z)
7.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
1106×add-sqr-sqrt
514×associate-*l*
470×*-un-lft-identity
440×times-frac
408×sqrt-prod
291×unswap-sqr
270×add-cube-cbrt
250×difference-of-squares
216×associate-*r*
180×prod-diff
122×*-commutative
100×distribute-lft-out--
89×swap-sqr
22×associate-/l*
20×associate-/r*
18×add-exp-log add-cbrt-cube
15×fma-neg
10×pow1
6×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log clear-num div-inv
Counts
4 → 789
Calls
4 calls:
19.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
83.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
86.0ms
(sqrt (- (* z z) (* t a)))

simplify135.0ms

Algorithm
egg-herbie
Counts
801 → 801
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0172810568
150019141

prune803.0ms

Filtered
801 candidates to 275 candidates (34.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New78813801
Fresh000
Picked101
Done000
Total78913802

Merged error: 2.9b

Counts
802 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
1.8b
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
3.0b
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
1659×add-sqr-sqrt
700×times-frac
625×sqrt-prod
547×unswap-sqr
536×*-un-lft-identity
485×associate-*r*
446×associate-*l*
350×difference-of-squares
255×cbrt-prod
254×add-cube-cbrt
140×distribute-lft-out--
123×*-commutative
103×add-cbrt-cube
92×swap-sqr
74×cbrt-unprod
45×add-exp-log
40×associate-/r*
39×associate-*r/
34×associate-/l*
22×prod-exp
21×cbrt-undiv
14×pow1
8×div-exp
6×sqrt-div pow-prod-down
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×flip3-- clear-num un-div-inv flip--
2×frac-2neg div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 947
Calls
4 calls:
1.0ms
(cbrt y)
228.0ms
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
28.0ms
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
29.0ms
(sqrt (- (* z z) (* t a)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt y)
111.0ms
(* (* x (* (cbrt y) (cbrt y))) (/ (* (cbrt y) z) (sqrt (- (* z z) (* t a)))))
118.0ms
(/ (* (cbrt y) z) (sqrt (- (* z z) (* t a))))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify168.0ms

Algorithm
egg-herbie
Counts
959 → 959
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0247413815
1500212907

prune1.6s

Filtered
959 candidates to 471 candidates (49.1%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New9572959
Fresh01212
Picked011
Done000
Total95715972

Merged error: 2.9b

Counts
972 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite43.1s

Algorithm
rewrite-expression-head
Rules
322908×add-sqr-sqrt
196860×cbrt-prod
187282×unswap-sqr
75350×times-frac
47407×sqrt-prod
32206×swap-sqr
15286×*-un-lft-identity
14740×associate-*l*
12950×associate-*r*
9757×*-commutative
8945×associate-/r*
7476×associate-*r/
7226×frac-times
6738×difference-of-squares
6141×cbrt-unprod
6037×add-cbrt-cube
5089×associate-/l*
4948×distribute-lft-out--
4684×add-cube-cbrt
1986×cbrt-undiv
310×add-exp-log
206×clear-num
205×frac-2neg
192×prod-exp
159×associate-*l/
66×div-exp
28×pow1
20×sqrt-div
15×pow-prod-down
14×cbrt-div
10×flip3-- associate-/r/ flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 un-div-inv
2×div-inv
Counts
4 → 50461
Calls
4 calls:
27.2s
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
25.0ms
(sqrt (- (* z z) (* t a)))
28.0ms
(sqrt (- (* z z) (* t a)))
26.0ms
(sqrt (- (* z z) (* t a)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (* x (* (cbrt y) (cbrt y))) (* (/ (* (cbrt (cbrt y)) (cbrt (cbrt y))) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (* (cbrt (cbrt y)) z) (cbrt (sqrt (- (* z z) (* t a)))))))
61.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify23.5s

Algorithm
egg-herbie
Counts
50473 → 50473
Iterations

Useful iterations: 0 (455.0ms)

IterNodesCost
0171133096265

prune1.2m

Filtered
50473 candidates to 11015 candidates (21.8%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New50472150473
Fresh01313
Picked101
Done011
Total504731550488

Merged error: 2.9b

Counts
50488 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (* x y))
7.6b
(cbrt (* x y))
21.2b
(sqrt (- (* z z) (* t a)))
21.2b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
34×sqrt-prod
28×*-un-lft-identity
24×cbrt-prod
20×difference-of-squares
16×unswap-sqr
14×associate-*l*
12×add-cube-cbrt
8×distribute-lft-out--
6×pow1 associate-*r* *-commutative
4×add-exp-log expm1-log1p-u sqrt-div swap-sqr add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow1/3 flip--
Counts
4 → 106
Calls
4 calls:
4.0ms
(cbrt (* x y))
4.0ms
(cbrt (* x y))
29.0ms
(sqrt (- (* z z) (* t a)))
26.0ms
(sqrt (- (* z z) (* t a)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(cbrt (* x y))
72.0ms
(cbrt (* x y))
62.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify75.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0285712
1781694
22423664
35003656

prune307.0ms

Filtered
118 candidates to 82 candidates (69.5%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1171118
Fresh11213
Picked011
Done011
Total11815133

Merged error: 2.9b

Counts
133 → 15

regimes553.0ms

Accuracy

84.7% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.7b

bsearch83.0ms

Steps
ItersRangePoint
8
1.2618041718263966e+72
6.888002027293982e+75
3.978479322381757e+75
6
-1.8994188819116795e+129
-2.225823687745991e+128
-2.852449342955382e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13715
23715

end0.0ms

sample792.0ms

Algorithm
intervals
Results
343.0ms8834×body80valid
101.0ms2843×body80nan