Details

Time bar (total: 32.6s)

sample72.0ms

Algorithm
intervals
Results
22.0ms291×body80nan
18.0ms256×body80valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05017
110817
238917
3176117
4500217

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))
2.6b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.7b
(/ (* z (sqrt (+ t a))) t)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
63×prod-diff
62×associate--r+
49×add-sqr-sqrt
45×add-cube-cbrt
36×times-frac
31×distribute-rgt-in distribute-lft-in
20×frac-sub
16×add-exp-log add-cbrt-cube
15×distribute-lft-out
12×div-inv
9×flip3-- flip--
8×frac-times associate-*r/
7×fma-neg associate-*r*
6×pow1 add-log-exp
5×flip3-+ sqrt-prod flip-+
4×cbrt-undiv expm1-log1p-u sqrt-div div-exp associate-/r* log1p-expm1-u associate-/l*
3×sub-neg associate-*l* prod-exp cbrt-unprod
2×frac-2neg associate-*l/ associate--l+ clear-num associate-/l/ unswap-sqr
1×diff-log pow-prod-down *-commutative
Counts
4 → 179
Calls
4 calls:
11.0ms
(* z (sqrt (+ t a)))
3.0ms
(/ 2.0 (* t 3.0))
40.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.0ms
(/ (* z (sqrt (+ t a))) t)

series326.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* z (sqrt (+ t a)))
15.0ms
(/ 2.0 (* t 3.0))
172.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
77.0ms
(/ (* z (sqrt (+ t a))) t)

simplify51.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013772637
150012324

prune1.2s

Filtered
191 candidates to 137 candidates (71.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt t)
0.6b
(cbrt t)
0.6b
(cbrt t)
1.8b
(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (- b c))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt t)
0.0ms
(cbrt t)
1.0ms
(cbrt t)
0.0ms
(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (- b c))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt t)
169.0ms
(cbrt t)
163.0ms
(cbrt t)
314.0ms
(fma (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)) (- (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (- b c))))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
0144371
1339322
21169312
35002308

prune407.0ms

Filtered
61 candidates to 54 candidates (88.5%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

3.6b
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
4.2b
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
7.4b
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
30.6b
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
766×associate-*l/
764×associate-*r/
524×frac-sub
498×flip3-- flip--
364×frac-times
240×sqrt-div
162×associate-/l/
120×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
24×distribute-rgt-in distribute-lft-in
14×pow1
12×prod-exp cbrt-unprod associate--r+
9×sub-neg prod-diff
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*l*
6×pow-prod-down add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×times-frac associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×frac-2neg fma-neg diff-log div-sub clear-num associate-/r* div-inv difference-of-squares
Counts
4 → 455
Calls
4 calls:
97.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
15.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
159.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
298.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
183.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
47.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
581.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
705.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify323.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0490623936
1500123936

prune6.0s

Filtered
467 candidates to 433 candidates (92.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
3.6b
(* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))
7.4b
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0)))))
30.6b
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
2884×associate-*l/
2718×associate-*r/
1808×frac-sub
1608×flip3-- flip--
1588×frac-times
750×sqrt-div
681×flip3-+ flip-+
500×associate-/l/
110×sub-div
44×add-exp-log add-cbrt-cube
30×pow1
24×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
18×pow-prod-down
12×associate--r+
9×sub-neg prod-diff
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp associate-*l* log1p-expm1-u
3×times-frac associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×frac-2neg fma-neg diff-log div-sub clear-num associate-/r* div-inv
Counts
4 → 1188
Calls
4 calls:
51.0ms
(* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
253.0ms
(* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))
281.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0)))))
413.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0)))
186.0ms
(* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))
574.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0)))))
919.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify655.0ms

Algorithm
egg-herbie
Counts
1200 → 1200
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0500267797

prune14.8s

Filtered
1200 candidates to 1165 candidates (97.1%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes306.0ms

Accuracy

14.5% (1.1b remaining)

Error of 1.9b against oracle of 0.8b and baseline of 2.1b

bsearch315.0ms

Steps
ItersRangePoint
8
2.1030767940956052e-274
4.458132482621783e-271
2.4818379584590413e-273
7
-1.8064347706140234e-199
-1.062326948166824e-200
-1.7561934868003836e-199

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08567
18767
28767

end0.0ms

sample1.8s

Algorithm
intervals
Results
606.0ms8000×body80valid
561.0ms7836×body80nan