Details

Time bar (total: 7.6s)

sample57.0ms

Algorithm
intervals
Results
19.0ms379×body80valid
15.0ms340×body80nan

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (19.0ms)

IterNodesCost
04012
19212
226912
366912
4156511
5285511
6500111

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ y 0.0007936500793651) z)
0.1b
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.2b
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
4.8b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
10×add-exp-log add-cbrt-cube
9×times-frac
8×pow1
7×associate-*l*
6×associate-*r*
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ associate-/l/ unswap-sqr
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv distribute-lft-out
Counts
4 → 86
Calls
4 calls:
9.0ms
(* (+ y 0.0007936500793651) z)
0.0ms
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
19.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
21.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series280.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ y 0.0007936500793651) z)
123.0ms
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
44.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
86.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0446778
11546696
25002694

prune368.0ms

Filtered
98 candidates to 79 candidates (80.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.2b
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b
(* (log x) (- x 0.5))
4.8b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt
116×*-un-lft-identity
101×prod-diff
88×add-cube-cbrt
68×associate-+r+
54×times-frac
22×distribute-rgt-in associate-+l+ distribute-lft-in
14×distribute-lft-out-- difference-of-squares
13×add-log-exp
10×add-exp-log flip3-- associate-*r/ add-cbrt-cube flip--
9×pow1
8×associate-*r* frac-add
7×associate-*l*
6×div-inv
5×sub-neg
4×expm1-log1p-u frac-sub log1p-expm1-u
3×diff-log associate-/r* sum-log associate-/l*
2×flip3-+ pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod flip-+ associate-/l/ unswap-sqr
1×cbrt-undiv +-commutative associate-+r- fma-def frac-2neg div-exp clear-num log-pow associate--r-
Counts
4 → 215
Calls
4 calls:
131.0ms
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
19.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
12.0ms
(* (log x) (- x 0.5))
24.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series519.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
45.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
253.0ms
(* (log x) (- x 0.5))
87.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify145.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012533523
148823081
250013081

prune817.0ms

Filtered
227 candidates to 156 candidates (68.7%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 0.0007936500793651))
0.3b
(* (cbrt (+ y 0.0007936500793651)) z)
0.3b
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
4.8b
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-div
34×associate-*l/
30×flip3-+ flip-+
28×frac-times
20×add-exp-log add-sqr-sqrt *-un-lft-identity
18×pow1
16×add-cube-cbrt
13×add-cbrt-cube
9×cbrt-prod times-frac pow-prod-down prod-exp cbrt-unprod
8×associate-*r/ associate-*l*
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×*-commutative associate-/l/ distribute-lft-out unswap-sqr
1×cbrt-undiv frac-2neg pow1/3 div-exp clear-num div-inv
Counts
4 → 124
Calls
4 calls:
2.0ms
(cbrt (+ y 0.0007936500793651))
11.0ms
(* (cbrt (+ y 0.0007936500793651)) z)
40.0ms
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
133.0ms
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

series417.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(cbrt (+ y 0.0007936500793651))
205.0ms
(* (cbrt (+ y 0.0007936500793651)) z)
33.0ms
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
91.0ms
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

simplify72.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07651800
125701613
250021538

prune575.0ms

Filtered
136 candidates to 93 candidates (68.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
0.3b
(cbrt (+ y 0.0007936500793651))
0.9b
(pow (cbrt (+ y 0.0007936500793651)) 3)
4.8b
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
33×add-sqr-sqrt add-cube-cbrt
30×times-frac
12×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
7×add-exp-log unpow-prod-down cube-prod
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u neg-mul-1 cbrt-div log1p-expm1-u add-log-exp
3×pow-unpow distribute-lft-out associate-/l*
2×cube-div pow-pow flip3-+ pow1/3 flip-+
1×cbrt-undiv cube-mult pow-to-exp frac-2neg unpow3 div-exp pow-exp clear-num fma-udef div-inv rem-cube-cbrt sqr-pow
Counts
4 → 119
Calls
4 calls:
0.0ms
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
2.0ms
(cbrt (+ y 0.0007936500793651))
5.0ms
(pow (cbrt (+ y 0.0007936500793651)) 3)
4.0ms
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

series535.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
94.0ms
(cbrt (+ y 0.0007936500793651))
145.0ms
(pow (cbrt (+ y 0.0007936500793651)) 3)
139.0ms
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

simplify77.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06361558
127831460
250011442

prune598.0ms

Filtered
131 candidates to 99 candidates (75.6%)
Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

regimes766.0ms

Accuracy

88.9% (0.3b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 6.0b

bsearch81.0ms

Steps
ItersRangePoint
8
2.7511213928627524e+19
1.2829957220891316e+24
5.071721045019439e+20

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05230
15930
25930

end0.0ms

sample1.6s

Algorithm
intervals
Results
602.0ms11726×body80valid
512.0ms11581×body80nan