Details

Time bar (total: 39.4s)

sample609.0ms

Algorithm
intervals
Results
208.0ms95×body2560valid
198.0ms100×body1280valid
127.0ms60×body10240exit
24.0ms31×body640valid
15.0ms316×pre80true
9.0ms17×body320valid
2.0ms9×body80valid
1.0ms4×body160valid

simplify189.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
189.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.0b

localize41.0ms

Local error

Found 4 expressions with local error:

29.0b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
21.7b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.3b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* eps a))

rewrite51.0ms

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/
Counts
4 → 108
Calls
4 calls:
Slowest
20.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
18.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
10.0ms
(* (expm1 (* (+ a b) eps)) eps)
1.0ms
(expm1 (* eps a))

series880.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
569.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
159.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
118.0ms
(* (expm1 (* (+ a b) eps)) eps)
34.0ms
(expm1 (* eps a))

simplify9.1s

Counts
94 → 120
Calls
94 calls:
Slowest
613.0ms
(- (- (+ (log (expm1 (* (+ a b) eps))) (log eps)) (log (expm1 (* eps a)))) (log (expm1 (* eps b))))
557.0ms
(/ (/ (* (* (* (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))))
531.0ms
(/ (/ (* (* (* (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))))
456.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
442.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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
Counts
1 → 35
Calls
1 calls:
Slowest
11.0ms
(+ (/ 1 a) (/ 1 b))

series17.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
17.0ms
(+ (/ 1 a) (/ 1 b))

simplify366.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
62.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
20.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))
20.0ms
(+ (/ 1 b) (/ 1 a))
19.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
18.0ms
(/ (sqrt 1) (* (cbrt a) (cbrt a)))

prune352.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

15.3b
(/ (+ b a) (* a b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-cbrt-cube add-exp-log
4×times-frac associate-/l*
3×add-sqr-sqrt add-cube-cbrt
2×cbrt-undiv div-exp distribute-lft-out associate-/l/
1×expm1-log1p-u pow1 clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 28
Calls
1 calls:
Slowest
20.0ms
(/ (+ b a) (* a b))

series56.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
56.0ms
(/ (+ b a) (* a b))

simplify690.0ms

Counts
19 → 31
Calls
19 calls:
Slowest
219.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
193.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
74.0ms
(- (log (+ b a)) (+ (log a) (log b)))
50.0ms
(+ (pow b 3) (pow a 3))
40.0ms
(- (log (+ b a)) (log (* a b)))

prune205.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

10.1b
(* (/ 1 a) (/ (+ b a) b))
0.0b
(/ (+ b a) b)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
42×*-un-lft-identity
40×times-frac
26×add-exp-log add-cube-cbrt
16×add-cbrt-cube associate-*r*
13×associate-*l*
9×div-exp
8×prod-exp
7×distribute-lft-out
6×unswap-sqr
5×cbrt-undiv
4×pow1 cbrt-unprod associate-/l*
3×associate-/r* div-inv
2×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
2 → 98
Calls
2 calls:
Slowest
36.0ms
(* (/ 1 a) (/ (+ b a) b))
14.0ms
(/ (+ b a) b)

series111.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
67.0ms
(* (/ 1 a) (/ (+ b a) b))
44.0ms
(/ (+ b a) b)

simplify4.2s

Counts
93 → 104
Calls
93 calls:
Slowest
342.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b))
323.0ms
(* (/ (* (* 1 1) 1) (* (* a a) a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
323.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
214.0ms
(+ (- 0 (log a)) (log (/ (+ b a) b)))
203.0ms
(+ (log (/ 1 a)) (- (log (+ b a)) (log b)))

prune882.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes131.0ms

Accuracy

-7.9% (3.7b remaining)

Error of 3.7b against oracle of 0.0b and baseline of 3.4b

bsearch218.0ms

end0.0ms

sample19.5s

Algorithm
intervals
Results
5.8s2590×body2560valid
5.7s3375×body1280valid
5.2s2013×body10240exit
1.3s1047×body640valid
612.0ms10013×pre80true
335.0ms389×body320valid
106.0ms456×body80valid
53.0ms143×body160valid