Details

Time bar (total: 54.9s)

sample531.0ms

Algorithm
intervals
Results
171.0ms72×body2560valid
146.0ms114×body1280valid
133.0ms41×body10240exit
36.0ms39×body640valid
15.0ms297×pre80true
4.0ms8×body320valid
4.0ms19×body80valid
2.0ms4×body160valid

simplify511.0ms

Calls
1 calls:
Slowest
511.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize56.0ms

Local error

Found 4 expressions with local error:

24.2b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
14.1b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.3b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
8×associate-/l*
7×cbrt-undiv div-exp
6×pow1 associate-/r* div-inv
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod
2×clear-num frac-2neg
1×expm1-log1p pow-prod-down *-commutative expm1-udef unswap-sqr associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
8.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
5.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series951.0ms

Calls
4 calls:
Slowest
601.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
157.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
118.0ms
(* (expm1 (* (+ a b) eps)) eps)
75.0ms
(expm1 (* (+ a b) eps))

simplify9.3s

Calls
94 calls:
Slowest
638.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
495.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
393.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
361.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))
315.0ms
(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
5×div-inv
3×add-log-exp
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
11.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

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

simplify385.0ms

Calls
27 calls:
Slowest
61.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
26.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
21.0ms
(+ (/ 1 a) (/ 1 b))
19.0ms
(+ (/ 1 a) (/ 1 b))
19.0ms
(+ (/ 1 a) (/ 1 b))

prune308.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize34.0ms

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)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
114×cbrt-prod
81×distribute-lft-out
60×div-inv
42×times-frac
37×add-sqr-sqrt
33×cbrt-div swap-sqr
29×add-cube-cbrt
13×associate-*r* associate-*l*
11×pow1 flip3-+ frac-add flip-+
9×frac-times pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l/ associate-*r/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
86.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
16.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
14.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
11.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series479.0ms

Calls
4 calls:
Slowest
136.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
130.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
112.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
101.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify12.1s

Calls
187 calls:
Slowest
511.0ms
(* (cbrt (+ (* 1 b) (* a 1))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
466.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (/ 1 a) (/ 1 b))))
433.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
431.0ms
(* (cbrt (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))) (cbrt (* a b)))
429.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

13.9b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
7.0b
(/ (* eps b) a)
0.0b
(expm1 (* eps b))
0.0b
(+ (/ (* eps b) a) eps)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
18×times-frac
17×add-sqr-sqrt add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×fma-def
6×associate-/r* add-log-exp
5×log1p-expm1-u distribute-lft-out associate-/l*
4×expm1-log1p-u pow1 insert-posit16
3×cbrt-undiv div-exp div-inv
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×+-commutative expm1-log1p sum-log prod-exp cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
34.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
19.0ms
(+ (/ (* eps b) a) eps)
18.0ms
(/ (* eps b) a)
1.0ms
(expm1 (* eps b))

series236.0ms

Calls
4 calls:
Slowest
114.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
47.0ms
(expm1 (* eps b))
39.0ms
(+ (/ (* eps b) a) eps)
36.0ms
(/ (* eps b) a)

simplify4.2s

Calls
66 calls:
Slowest
472.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
374.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
333.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
273.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
255.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))

prune965.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes165.0ms

Accuracy

-9.6% (3.7b remaining)

Error of 3.8b against oracle of 0.0b and baseline of 3.4b

bsearch327.0ms

end0.0ms

sample20.5s

Algorithm
intervals
Results
7.1s2649×body2560valid
5.9s3350×body1280valid
4.8s1879×body10240exit
989.0ms1067×body640valid
749.0ms349×body320valid
593.0ms9879×pre80true
119.0ms462×body80valid
48.0ms123×body160valid