Details

Time bar (total: 41.6s)

sample477.0ms

Algorithm
intervals
Results
159.0ms88×body2560valid
135.0ms58×body10240exit
108.0ms97×body1280valid
29.0ms40×body640valid
14.0ms314×pre80true
5.0ms10×body320valid
2.0ms17×body80valid
1.0ms4×body160valid

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
244.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.8b

localize52.0ms

Local error

Found 4 expressions with local error:

31.1b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
16.5b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite47.0ms

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
21.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
17.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
7.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
649.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
153.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
138.0ms
(* (expm1 (* (+ a b) eps)) eps)
69.0ms
(expm1 (* (+ a b) eps))

simplify9.9s

Counts
94 → 120
Calls
94 calls:
Slowest
691.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
565.0ms
(/ (/ (* (* (* (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))))
477.0ms
(/ (/ (* (* (* (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))))
428.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
396.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 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))

series12.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify438.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
54.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
25.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
24.0ms
(/ (sqrt 1) (* (cbrt a) (cbrt a)))
21.0ms
(+ (/ 1 a) (/ 1 b))
21.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))

prune335.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

12.6b
(/ (+ b a) (* a b))

rewrite35.0ms

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
34.0ms
(/ (+ b a) (* a b))

series49.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
49.0ms
(/ (+ b a) (* a b))

simplify753.0ms

Counts
19 → 31
Calls
19 calls:
Slowest
238.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
186.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
68.0ms
(- (log (+ b a)) (log (* a b)))
42.0ms
(- (* b b) (* a a))
39.0ms
(- (log (+ b a)) (+ (log a) (log b)))

prune267.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

31.1b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
17.0b
(cbrt (expm1 (* eps b)))
17.0b
(cbrt (expm1 (* eps b)))
17.0b
(cbrt (expm1 (* eps b)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac pow1/3
2×cbrt-undiv div-exp
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 66
Calls
4 calls:
Slowest
17.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
2.0ms
(cbrt (expm1 (* eps b)))
1.0ms
(cbrt (expm1 (* eps b)))
1.0ms
(cbrt (expm1 (* eps b)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
137.0ms
(cbrt (expm1 (* eps b)))
122.0ms
(cbrt (expm1 (* eps b)))
118.0ms
(cbrt (expm1 (* eps b)))

simplify4.5s

Counts
35 → 78
Calls
35 calls:
Slowest
445.0ms
(pow (- (exp (* eps b)) 1) 1/3)
412.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
404.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
374.0ms
(pow (- (exp (* eps b)) 1) 1/3)
371.0ms
(pow (- (exp (* eps b)) 1) 1/3)

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (3.3b remaining)

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

bsearch1.0ms

end0.0ms

sample19.8s

Algorithm
intervals
Results
6.0s2545×body2560valid
5.7s2033×body10240exit
5.7s3466×body1280valid
1.1s1065×body640valid
554.0ms10034×pre80true
226.0ms353×body320valid
105.0ms448×body80valid
48.0ms124×body160valid