Details

Time bar (total: 38.3s)

sample563.0ms

Algorithm
intervals
Results
197.0ms72×body2560valid
177.0ms114×body1280valid
103.0ms41×body10240exit
37.0ms39×body640valid
15.0ms297×pre80true
5.0ms8×body320valid
4.0ms19×body80valid
2.0ms4×body160valid

simplify306.0ms

Calls
1 calls:
Slowest
306.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize62.0ms

Local error

Found 4 expressions with local error:

35.8b
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
0.5b
(* (expm1 (* eps b)) (expm1 (* eps a)))
0.3b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r*
2×cbrt-undiv div-exp prod-exp *-commutative cbrt-unprod
1×expm1-log1p clear-num associate-/r* frac-2neg times-frac pow-prod-down div-inv associate-/l* expm1-udef
Calls
4 calls:
Slowest
8.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
4.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))
3.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series869.0ms

Calls
4 calls:
Slowest
605.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
128.0ms
(* (expm1 (* (+ a b) eps)) eps)
78.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))
58.0ms
(expm1 (* (+ a b) eps))

simplify3.5s

Calls
31 calls:
Slowest
717.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps a))) (* (expm1 (* eps b)) (expm1 (* eps a)))) (* (expm1 (* eps b)) (expm1 (* eps a)))))
543.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))
435.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
354.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
250.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune983.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (/ 1 a) (/ 1 b))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×div-inv
4×fma-def distribute-lft-out
3×add-log-exp
2×add-sqr-sqrt add-cube-cbrt
1×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 log1p-expm1-u
Calls
1 calls:
Slowest
5.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify153.0ms

Calls
12 calls:
Slowest
20.0ms
(+ (/ 1 b) (/ 1 a))
18.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 b) (/ 1 a))
16.0ms
(+ (/ 1 a) (/ 1 b))
14.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))

prune223.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
35×cbrt-prod
33×cbrt-div
31×*-un-lft-identity
20×div-inv distribute-lft-out
11×add-sqr-sqrt flip3-+ frac-add add-cube-cbrt flip-+
10×associate-*r* associate-*l*
9×frac-times pow1
7×pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
19.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
5.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
4.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
2.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series449.0ms

Calls
4 calls:
Slowest
126.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
117.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
114.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
93.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify10.2s

Calls
94 calls:
Slowest
502.0ms
(* (cbrt (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
485.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
462.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (/ 1 a) (/ 1 b))))
460.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
456.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (* 1 b) (* a 1))))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

14.6b
(/ (+ b a) (* a b))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity times-frac add-cbrt-cube add-exp-log add-cube-cbrt associate-/l*
2×associate-/l/
1×expm1-log1p-u pow1 cbrt-undiv clear-num associate-/r* frac-2neg flip3-+ div-exp flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
1 calls:
Slowest
7.0ms
(/ (+ b a) (* a b))

series60.0ms

Calls
1 calls:
Slowest
60.0ms
(/ (+ b a) (* a b))

simplify321.0ms

Calls
15 calls:
Slowest
138.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
34.0ms
(- (* b b) (* a a))
30.0ms
(- (log (+ b a)) (log (* a b)))
25.0ms
(/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)
17.0ms
(+ (/ 1 b) (/ 1 a))

prune214.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes135.0ms

Accuracy

16.3% (2.9b remaining)

Error of 2.9b against oracle of 0.0b and baseline of 3.4b

bsearch314.0ms

end0.0ms

sample18.7s

Algorithm
intervals
Results
6.7s2649×body2560valid
6.0s3350×body1280valid
3.8s1879×body10240exit
1.1s1067×body640valid
492.0ms9879×pre80true
232.0ms349×body320valid
80.0ms462×body80valid
52.0ms123×body160valid