Details

Time bar (total: 1.8m)

sample604.0ms

Algorithm
intervals
Results
178.0ms73×body10240exit
171.0ms72×body2560valid
153.0ms110×body1280valid
41.0ms33×body640valid
17.0ms330×pre80true
11.0ms16×body320valid
4.0ms19×body80valid
3.0ms7×body160valid

simplify302.0ms

Calls
1 calls:
Slowest
302.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize30.0ms

Local error

Found 4 expressions with local error:

37.3b
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
0.1b
(* (expm1 (* eps b)) (expm1 (* eps a)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite23.0ms

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
15.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
5.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))
3.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series597.0ms

Calls
4 calls:
Slowest
416.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
87.0ms
(* (expm1 (* (+ a b) eps)) eps)
47.0ms
(expm1 (* (+ a b) eps))
46.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))

simplify3.6s

Calls
31 calls:
Slowest
682.0ms
(/ (* (* (* (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)))))
510.0ms
(/ (* (* (* (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)))))
406.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
377.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
324.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune950.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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))

series10.0ms

Calls
1 calls:
Slowest
10.0ms
(+ (/ 1 a) (/ 1 b))

simplify149.0ms

Calls
12 calls:
Slowest
25.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 a) (/ 1 b))
15.0ms
(+ (/ 1 a) (/ 1 b))
15.0ms
(+ (* 1 b) (* a 1))

prune231.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

27.1b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
14.1b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
8×associate-/l*
6×associate-/r* div-inv
5×log1p-expm1-u
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 add-log-exp
3×associate-*l*
2×clear-num frac-2neg
1×expm1-log1p *-commutative expm1-udef associate-/l/
Calls
4 calls:
Slowest
19.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
9.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
6.0ms
(* (expm1 (* (+ a b) eps)) eps)
1.0ms
(expm1 (* (+ a b) eps))

series694.0ms

Calls
4 calls:
Slowest
473.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
107.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
68.0ms
(* (expm1 (* (+ a b) eps)) eps)
46.0ms
(expm1 (* (+ a b) eps))

simplify6.3s

Calls
83 calls:
Slowest
456.0ms
(/ (/ (* (* (* (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))))
363.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
359.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
270.0ms
(- (log (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))) (log (expm1 (* eps a))))
267.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

39.8b
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
4.0b
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))
2.8b
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
2.3b
(+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
194×frac-add
165×associate-*r/ un-div-inv
144×frac-sub
138×associate-*l/
123×*-un-lft-identity
120×frac-times
98×associate-/r/
85×distribute-lft-out
84×unpow-prod-down cube-prod
83×div-inv
63×times-frac
54×sub-div
33×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
14×fma-def
13×add-log-exp
9×flip3-- flip--
6×add-cbrt-cube add-exp-log
5×sum-cubes
4×cube-div expm1-log1p-u pow1 flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×associate-+r+ associate-/r* sum-log associate-/l/
2×+-commutative sub-neg diff-log prod-diff
1×cube-mult cbrt-undiv clear-num associate-+r- frac-2neg distribute-rgt-out-- fma-neg unpow3 div-exp
Calls
4 calls:
Slowest
72.0ms
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
31.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
17.0ms
(+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))
15.0ms
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))

series106.0ms

Calls
4 calls:
Slowest
49.0ms
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
28.0ms
(+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))
17.0ms
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))
12.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))

simplify1.2m

Calls
556 calls:
Slowest
878.0ms
(+ (* (* 1 1) (* b b)) (* (* a a) (- (* (* 1 (/ 1 b)) b) (* b (/ 1 a)))))
866.0ms
(+ (* (* 1 1) (* b b)) (* (* a a) (- (* (/ 1 b) b) (* b (/ 1 a)))))
864.0ms
(+ (* (* 1 1) (* b b)) (* (* a a) (- (* (* (/ 1 b) 1) b) (* b (/ 1 a)))))
598.0ms
(/ (pow 1 3) (sqrt (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))))
540.0ms
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (sqrt (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))))

prune3.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

4.5% (3.2b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 3.4b

bsearch172.0ms

end0.0ms

sample12.7s

Algorithm
intervals
Results
3.8s2549×body2560valid
3.6s1954×body10240exit
3.5s3490×body1280valid
681.0ms1069×body640valid
619.0ms9956×pre80true
183.0ms311×body320valid
52.0ms455×body80valid
32.0ms128×body160valid