Details

Time bar (total: 29.5s)

sample488.0ms

Algorithm
intervals
Results
154.0ms112×body1280valid
128.0ms71×body2560valid
104.0ms63×body10240exit
34.0ms44×body640valid
15.0ms319×pre80true
3.0ms5×body320valid
3.0ms17×body80valid
3.0ms7×body160valid

simplify593.0ms

Calls
1 calls:
Slowest
593.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize28.0ms

Local error

Found 4 expressions with local error:

38.4b
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(* (expm1 (* eps b)) (expm1 (* eps a)))
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))

series649.0ms

Calls
4 calls:
Slowest
464.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
90.0ms
(* (expm1 (* (+ a b) eps)) eps)
55.0ms
(expm1 (* (+ a b) eps))
40.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))

simplify3.5s

Calls
31 calls:
Slowest
559.0ms
(/ (* (* (* (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)))))
534.0ms
(/ (* (* (* (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)))))
474.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
358.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))
355.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))

prune915.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

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
9.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

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

simplify149.0ms

Calls
12 calls:
Slowest
20.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
20.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 a) (/ 1 b))
16.0ms
(+ (/ 1 a) (/ 1 b))
15.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))

prune224.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

13.7b
(/ (+ b a) (* a b))

rewrite7.0ms

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))

series33.0ms

Calls
1 calls:
Slowest
33.0ms
(/ (+ b a) (* a b))

simplify340.0ms

Calls
15 calls:
Slowest
184.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
60.0ms
(- (log (+ b a)) (log (* a b)))
20.0ms
(- (* b b) (* a a))
12.0ms
(/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)
11.0ms
(+ (pow b 3) (pow a 3))

prune152.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a) (/ (cbrt (+ b a)) b))
0.6b
(cbrt (+ b a))
0.6b
(cbrt (+ b a))
0.6b
(cbrt (+ b a))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 cbrt-div add-cbrt-cube add-exp-log
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+
2×div-inv
1×frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
12.0ms
(* (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a) (/ (cbrt (+ b a)) b))
1.0ms
(cbrt (+ b a))
1.0ms
(cbrt (+ b a))
1.0ms
(cbrt (+ b a))

series490.0ms

Calls
4 calls:
Slowest
154.0ms
(cbrt (+ b a))
134.0ms
(cbrt (+ b a))
125.0ms
(cbrt (+ b a))
76.0ms
(* (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a) (/ (cbrt (+ b a)) b))

simplify2.3s

Calls
40 calls:
Slowest
429.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
381.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
365.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
310.0ms
(+ (log (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)) (log (/ (cbrt (+ b a)) b)))
111.0ms
(* (* (* (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a) (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)) (/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)) (* (* (/ (cbrt (+ b a)) b) (/ (cbrt (+ b a)) b)) (/ (cbrt (+ b a)) b)))

prune835.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (3.4b remaining)

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

bsearch394.0ms

end0.0ms

sample18.1s

Algorithm
intervals
Results
6.0s2563×body2560valid
5.1s3471×body1280valid
4.1s2049×body10240exit
1.4s1065×body640valid
749.0ms10053×pre80true
304.0ms331×body320valid
76.0ms452×body80valid
69.0ms122×body160valid