Details

Time bar (total: 42.9s)

sample471.0ms

Algorithm
intervals
Results
137.0ms78×body2560valid
113.0ms104×body1280valid
99.0ms67×body10240exit
55.0ms46×body640valid
29.0ms11×body320valid
13.0ms323×pre80true
2.0ms13×body80valid
1.0ms4×body160valid

simplify236.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
236.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.5b

localize44.0ms

Local error

Found 4 expressions with local error:

29.8b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
16.3b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (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/
Counts
4 → 108
Calls
4 calls:
Slowest
10.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
9.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
6.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
648.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
164.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
117.0ms
(* (expm1 (* (+ a b) eps)) eps)
80.0ms
(expm1 (* (+ a b) eps))

simplify9.7s

Counts
94 → 120
Calls
94 calls:
Slowest
552.0ms
(/ (/ (* (* (* (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))))
537.0ms
(/ (/ (* (* (* (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))))
394.0ms
(* (- (exp (* (+ a b) eps)) 1) eps)
372.0ms
(* (- (exp (* (+ a b) eps)) 1) eps)
370.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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
22.0ms
(+ (/ 1 a) (/ 1 b))

series21.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
21.0ms
(+ (/ 1 a) (/ 1 b))

simplify403.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
40.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
24.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
24.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
19.0ms
(+ (/ 1 b) (/ 1 a))
18.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
0.6b
(cbrt a)
0.6b
(cbrt a)
0.5b
(* (cbrt a) (cbrt a))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(* (cbrt a) (cbrt a))
1.0ms
(cbrt a)
1.0ms
(cbrt a)
1.0ms
(cbrt a)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(* (cbrt a) (cbrt a))
268.0ms
(cbrt a)
250.0ms
(cbrt a)
248.0ms
(cbrt a)

simplify1.0s

Counts
63 → 97
Calls
63 calls:
Slowest
161.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
154.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
136.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
117.0ms
(* (pow (pow a 2) 1/3) (pow (cbrt -1) 2))
93.0ms
(* (* (cbrt (cbrt a)) (cbrt (cbrt a))) (* (cbrt (cbrt a)) (cbrt (cbrt a))))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

16.0b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
6.3b
(/ (* eps b) a)
0.0b
(expm1 (* eps b))
0.0b
(+ (/ (* eps b) a) eps)

rewrite88.0ms

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
59.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
17.0ms
(/ (* eps b) a)
10.0ms
(+ (/ (* eps b) a) eps)
0.0ms
(expm1 (* eps b))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
44.0ms
(+ (/ (* eps b) a) eps)
39.0ms
(expm1 (* eps b))
28.0ms
(/ (* eps b) a)

simplify4.3s

Counts
66 → 106
Calls
66 calls:
Slowest
424.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
368.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
353.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
269.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
264.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (3.3b remaining)

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

bsearch2.0ms

end0.0ms

sample20.0s

Algorithm
intervals
Results
6.7s2521×body2560valid
5.4s3426×body1280valid
5.2s1940×body10240exit
1.3s1133×body640valid
552.0ms9942×pre80true
267.0ms336×body320valid
79.0ms453×body80valid
49.0ms133×body160valid