Details

Time bar (total: 50.8s)

sample683.0ms

Algorithm
intervals
Results
253.0ms124×body1280valid
179.0ms78×body2560valid
164.0ms66×body10240exit
27.0ms26×body640valid
18.0ms322×pre80true
8.0ms10×body320valid
4.0ms17×body80valid
1.0ms1×body160valid

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize62.0ms

Local error

Found 4 expressions with local error:

30.1b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
14.0b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* eps b))

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
21.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
17.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
11.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* eps b))

series946.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
653.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
134.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
118.0ms
(* (expm1 (* (+ a b) eps)) eps)
42.0ms
(expm1 (* eps b))

simplify8.6s

Counts
94 → 120
Calls
94 calls:
Slowest
601.0ms
(/ (/ (* (* (* (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))))
563.0ms
(/ (/ (* (* (* (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))))
355.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
333.0ms
(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))
322.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite24.0ms

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
23.0ms
(+ (/ 1 a) (/ 1 b))

series20.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
20.0ms
(+ (/ 1 a) (/ 1 b))

simplify380.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
68.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
22.0ms
(+ (/ 1 a) (/ 1 b))
21.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))
20.0ms
(/ (sqrt 1) (* (cbrt a) (cbrt a)))
18.0ms
(+ (/ 1 a) (/ 1 b))

prune341.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

13.3b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
5.5b
(/ (* eps b) a)
0.0b
(expm1 (* eps b))
0.0b
(+ (/ (* eps b) a) eps)

rewrite53.0ms

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
Counts
4 → 94
Calls
4 calls:
Slowest
33.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
10.0ms
(+ (/ (* eps b) a) eps)
8.0ms
(/ (* eps b) a)
0.0ms
(expm1 (* eps b))

series209.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
54.0ms
(+ (/ (* eps b) a) eps)
46.0ms
(expm1 (* eps b))
23.0ms
(/ (* eps b) a)

simplify4.1s

Counts
66 → 106
Calls
66 calls:
Slowest
477.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
350.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
293.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
274.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
225.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

30.1b
(/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a)))
14.0b
(/ (/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* eps (expm1 (* (+ b a) eps)))
0.0b
(expm1 (* eps b))

rewrite32.0ms

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
17.0ms
(/ (/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a))) (expm1 (* eps b)))
9.0ms
(/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a)))
5.0ms
(* eps (expm1 (* (+ b a) eps)))
0.0ms
(expm1 (* eps b))

series832.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
577.0ms
(/ (/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a))) (expm1 (* eps b)))
143.0ms
(/ (* eps (expm1 (* (+ b a) eps))) (expm1 (* eps a)))
60.0ms
(expm1 (* eps b))
51.0ms
(* eps (expm1 (* (+ b a) eps)))

simplify8.4s

Counts
94 → 120
Calls
94 calls:
Slowest
654.0ms
(/ (/ (* (* (* eps (expm1 (* (+ b a) eps))) (* eps (expm1 (* (+ b a) eps)))) (* eps (expm1 (* (+ b a) eps)))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
403.0ms
(/ (/ (* (* (* eps eps) eps) (* (* (expm1 (* (+ b a) eps)) (expm1 (* (+ b a) eps))) (expm1 (* (+ b a) eps)))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
369.0ms
(* (- (exp (* (+ a b) eps)) 1) eps)
363.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
355.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

-11.7% (3.7b remaining)

Error of 3.7b against oracle of 0.0b and baseline of 3.3b

bsearch369.0ms

end0.0ms

sample21.0s

Algorithm
intervals
Results
6.7s2594×body2560valid
6.3s3482×body1280valid
5.0s1942×body10240exit
1.1s9946×pre80true
1.0s1016×body640valid
217.0ms344×body320valid
162.0ms442×body80valid
56.0ms126×body160valid